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ELEMENTS 

OF 

ASTRONOMY, 

ILLUSTRATED 
FOR  THE  USE  OF 

SCHOOLS  AND  ACADEMIES, 

WITH  QUESTIONS. 

— Q^^J© — 

BY  JOHN  H.  WILKINS,  A.  M 


"  I  shall  straight  conduct  you  to  a  hill-side,  laborious  indeed  at  the  first  ac- 
cent; but  else  so  smooth,  so  green,  so  full  of  goodly  prospect  and  melodious 
sounds  on  every  side,  that  the  harp  of  Orpheus  was  not  more  charming." 

Millon. 

STEREOTYPE  EDITION. 


BOSTON: 
PUBLISHED  BY   HILLIARD,   GRAY   AND  CO. 


DISTRICT  OF  MASSACHUSETTS,  TO  WIT. 

District  Clerk's  Office, 
BE  IT  REMEMBERED,  That  on  the  fifteenth  day  of  February, 
A.  D.  18'23,  and  in  the, forty-seventh  year  of  the  independence  of  the 
United  States  of  America,  J.  H.  Wilkins,  of  tlie  said  district,  has  de- 
posited in  this  office  the  title  of  a  l)ook,  the  right  whereof  he  claims 
as  author,  in  the  words  following-^  to  wit : 

"  Elements  of  Astronomy,  illustrated  with  plates,  for  the  use  of 
schools  and  academies  ;  with  questions.  By  John  H.  Wilkins,  A.  M. 
— "  We  shall  lead  you  to  a  hill-side,  laborious  indeed  in  the  first  as- 
cent ;  but  else  so  smooth,  so  greeny  so  full  of  goodly  prospects,  that 
the  harp  of  Orpheus  were  not  more  charming."  Milton. 

In  conformity  to  the  act  of  the  Congress  of  the  United  States,  en 
titled  "  An  act  for  the  encouragement  of  learning,  by  securing  the 
copies  of  maps,  charts,  and  books,  to  the  authors  and  proprietors  of 
such  copies,  during  the  times  therein  mentioned  ;"  and  also  tu  an  act, 
entitled  '•  An  c^ct  supplementary  to  an  act,  entitled  An  act  ff  r  the  en- 
couragement of  learning,  by  securing  the  copies  of  maps,  charts,  and 
books,  to  the  authors  and  proprietors  of  such  copies,  during  the 
times  therein  mentioned,  and  extending  the  benefits  thereof  to  the 
arts  of  designing,  engraving,  and  etching  historical  and  other  prints." 

JOHN  W.  DAVIS, 
Clerk  of  the  District  of  Massachusetts. 


Ri:CO]M£I»:ZlH£>ATIONS. 


Mr  Wilkins'  elementary  work  on  astronomy  appears  to  us  to  be 
made  upon  an  excellent  plan,  in  which  he  adopts  the  most  recent 
and  approved  distribution  of  the  subject.  The  several  parts  are 
arranged  in  a  simple  and  clear  method,  and  the  leading  facts  and 
principles  of  the  science  judiciously  selected  and  concisely  stated. 
It  contains  much  matter  within  a  narrow  compass,  embrticing  such 
recent  discoveries  and  results,  as  properly  come  within  the  author's 
plan  It  is  well  adapted  to  the  purposes  of  instruction,  and  will,  we 
have  no  doubt,  be  found  to  be  vei  /  convenient  and  useful  by  those 
teachers,  who  may  put  it  into  the  hands  of  pupils  of  an  age  and  pre- 
vious attainment?  to  cualify  them  for  this  study. 

ELISHA  CLAPP. 
WILLARD  PHILLIPS 


Dear  Sir, 
I  HAVE   examined  your  treatise  on  astronomy,   and  I  think  thai 
subject  is  better  explained,  and  that  more  matter  is  contained  in  tlyq, 
than  in  any  other  book  of  the  kind,  with  which  I  am  acquainted     \ 
therefore  cheerfully  recommend  it  to  the  patronage  of  the  public. 
With  respect,  sir, 

Your  obedient  servant, 

WARREN  COLBURN 
Mr.  J.  H.  Wilkins. 
Boston,  14  June  J  1822. 


Wilkins'  Elements  of  Astronomy,  by  presenting  in  a  concise,  but 
pcYspicuous  and  familiar  manner,  the  descriptive  and  physical  branch- 
es of  llie  science,  and  rejecting  what  is  merely  mechanical,  exhibits 


IV  RECOMMENDATIONS. 

to  the  student  all  that  is  most  valuable  and  interesting  to  the  youth 
ful  mind  in  this  sublime  department  of  human  knowledge. 

WALTER  R.  JOHNSON, 
Principal  of  the  Academy^  Gcrmantown^ 
Gcrmantowrtj  (Penn.)  5th  June,  1823. 


Having  examined  the  work  above  described,  I  unite  in  opmion  with 
Walter  R.  Johnson  concerning  its  merits. 

ROBERTS  VAUX. 
Philadelphia f  Hth  Mo,  11,  1823. 


Messrs.  Cummings,  Hilliard,  S^  Co, 

Having  been  partially  engaged  in  giving  instruction  to  youth,  for 
Ihe  last  fifteen  years,  it  has  been  necessary  for  me  to  examine  all  the 
Lreatises  on  education  which  came  within  my  reach.  Among  other 
treatises  examined,  there  have  been  several  on  Astronomy.  Of  these, 
the  "  Elements  of  Astronomy,  by  John  H.  Wilkins,  A.  M."  recentlv 
published  by  you,  is,  in  my  opinion,  decMedly  the  best.  I  have  ac- 
cordingly introduced  it  into  my  Seminary,  and  find  it  well  calculated 
to  answer  its  intended  purpose,  by  plain  illustrations  to  lead  youn<< 
persons  to  a  knowledge  of  that  most  interesting  science. 

J.  L.  BLAKE, 
Principal  of  Lit.  Sem.for  Young  Ladies 
Boston,  Jan.  5, 1825. 


DIRECTIONS  FOR  PLACING  THE  PLATES. 

COPPERPLATES. 

Frontispiece  to  front  title  page. — All  the  rest  in  order  at  the  end. 

WOOD   CUTS. 

Relative  sizes  of  the  Planets,                   .  -             -             Pao-o  7 

Telescopic  Appearances  of  Venus,         -  -            -            -        It 

"                 "                   Mars,           -  -             -             -         i7 

"                 "                  Jupiter,       -  -                          -        -.0 


ADVERTISEMENT 


TO  THE  SECOND  EDITION. 


The  rapid  sale  of  the  first  edition  of  this  work,  ths 
author  is  willing  to  attribute  to  the  obvious  public  desi- 
deratum of  a  work  of  this  kind,  rather  than  to  any  pe- 
culiar merit  of  his  production.  He  is  not  the  first,  nor 
probably  will  he  be  the  last,  to  form  a  more  correct 
judgment  of  what  the  public  need,  than  of  his  own 
ability  to  supply  that  deficiency.  The  encouragement 
which  he  has  received,  has,  however,  induced  him  to 
correct  and  somewhat  enlarge  his  work.  A  great  num- 
ber of  facts,  omitted  in  the  first  edition,  are  noticed  in 
this,  both  in  the  Descriptive  and  Physical  part.  To 
relieve  the  pupil  from  a  dry  narration  of  facts,  or  ab 
stract  illustration  of  principles,  the  author  has  subjoined 
to  their  proper  sections  and  articles,  a  popular  descrip- 
tion of  several  of  the  most  striking  natural  appearances 
and  phenomena.  He  has  also  greatly  increased  the 
number  of  questions.  Upon  the  whole,  he  feels  confi- 
dent, that  the  relative  value  of  his  work  is  not  diminish- 
ed by  having  its  size  increased. 

Several  instructers  have  suggested,  that  it  might  be 
usefid  to  subjoin  Tables  for  calculating  eclipses.  On 
this  subject  the  author  would  only  remark,  that  these 
Tables  and  the  necessary  instructions  for  applying  them, 
would  swell  the  work  to  a  size,  that  v;ould  in  a  consi- 
derable decrree   defeat  the  objects  of  its  publication 

1* 


VI  ADVERTISEMENT. 

Moreover,  he  cannot  very  highly  appreciate  the  value 
oi  mechanical  rules  for  calculating  eclipses,  while  the 
grounds  and  reasons  of  those  rules,  and  of  the  tables^  to 
which  they  refer,  are  not  understood ;  and  nothing  but 
mechanical  rules  can  here  be  expected.  To  a  vast  ma- 
jority of  pupils,  an  understanding  of  the  reasons  and 
principles  of  these  rules  and  tables  would  be  much 
more  useful  than  the  ability  to  apply  them. 

It  is  an  evil  to  have  frequent  alterations  in  school 
books  of  any  kind.  In  some  it  is  unpardonable.  Bui; 
it  is  a  still  greater  evil  to  have  a  book  remain  imperfect, 
while  it  is  in  the  power  of  the  author  to  improve  it,  and 
the  book  is  worth  the  labour.  This  is  particularly  true 
with  regard  to  books  like  this.  New  facts  in  astronomy 
are  continually  coming  into  notice,  which  modify  and 
limit  the  application  of  established  principles.  New 
data  for  intricate  calculations  are  derived  from  constant 
observation.  Hence  many  things,  w^hich  we  now  sup- 
pose to  be  true  or  nearly  so,  may  in  a  short  time  be 
found  to  be  false,  or  true  only  under  certain  circumstan- 
ces. New  and  happy  illustrations  of  difficult  subjects 
may  also  be  suggested.  All  these  wdll  cause  a  difference 
in  the  different  editions  of  the  same  w  ork.  The  author, 
tlierefore,  cannot  promise  that  future  editions  shall  not 
be  "  improved."  He  wdll,  however,  endeavour  to  make 
no  alterations,  which  are  not  dictated  by  real  utility 

Boston,  Feb.  14,  1823. 


CONTENTS. 


Introduction  _  -  -.  •  ^ 

BOOK  I. 

Chap.  I. 

Sect.  I.  Of  the  Solar  System  in  general 
Sect.  II.   Of  the  Sun 

Sect.  III.   Of  Mercury  -             •             .              lo 

Sect.  IV.    Of  Venus  -             -             •       ; . 

Sect.  V.   Of  the  Earth  -                           -              13 

Of  the  Moon  -             -             -         3 

Sect.  VI.   Of  Mars  -             -             -              .6 
Sect.  VII.   Of  Vesta,  Juno,  PaMas,  and  Ceres      -       17 

Sect.  VIII.  Of  Jupiter  -             -             -              18 

Sect.  IX.   Of  Saturn     -  -             -             -       20 

Sect.  X.   Of  Uranus  -             -             -             21 

Sect.  XI.   Of  Comets     -  -             -             -       23 

Sect.  XII.  Of  the  Stars  ...             25 

CHAP.  II. 

Of  Latitude  and  Longitude  -  -  -       32 

CHAP.  III. 

Sect.  I. — Of  phenomena  arising  from  the  situation 
of  the  Earth  in  the  Solar  System 

Art.  1. — Of  the  different  apparent  motions  and  mag- 
nitudes of  the  other  planets  -  48 

Art.  2.— Of  Eclipses  -         -  .  -       50 


VIll  CONTENTS- 

Sect.  II.   Of  Bay  and  JVight              -             -  56 

Sect.  III.  ^rt,  1. — Merration  of  light    -              -  59 

Art.  2. — The  Seasons              -             .             .  60 

Art.  3. — Equation  of  time             -              -              -  63 

Art.  4. — Of  the  Harvest  Moon  -  -  69 
ij^^CT.  IV.  Of  phenomena  arising  from  the  Earth''^ 

atmosphere       -              -              -  72 

Sect.  V.    Of  Parallax   -             -             -             -  79 

BOOK  II. 

Sttr  action  -  -  -  -  87 
Sect.  I.   Of  the  motion  of  heavenly  bodies  in  their 

orbits  -  -  -  -  90 
Sect.  II.   Of  the  retrograde  motion  of  the  Moon^s 

nodes      -              -              -              -  94 

Shict.  III.   Of  Irregidar  Motions               -              -  95 

Sfct.  IV.   Of  the  spheroidal  figure  of  the  planets  101 

Sect.  V.  Of  the  precession  of  the  equinoxes          -  103 

Sect.  VI.   Of  the  Tides       -             -             -  105 

APPENDIX. 

Sect.  I.   Of  Meteors             -              -              -  109 

Sect.  II.   Of  the  different  Systems           -              -  115 

Sect.  III.   Of  Leap  Year   -             -             -  117 

Sect.  IV.  Of  Old  and  JVew  Style          -             -  118 

Sect.  V.   Of  Cycles              -             -             -  118 

Sect.  VI.   Of  the  Dominical  Letter         -             -  121 

Sect.  VII.  Of  Epact           -             -             .  125 
Sect.  VIII    Problems 
Art.  1. — Problems  to   be  solved  by   the    Terrestrial 

Globe                  -             -             .  126 

Art.  2. — Problems  to  be  solved  by  the  Celestial  Globe  134 

Questions    -              -              -              -             -  137 


INTRODUCTION. 


1.  The  first  change  in  nature,  which  the  eye,  just 
opened  upon  the  things  of  this  world,  notices,  is  that  of 
light  and  shade,  from  day  to  night  and  from  night  to  day. 
The  beams  of  the  morning  awake  the  infant  from  the 
slumber  of  the  cradle,  and  call  him  forth  to  activity  and 
life  ;  the  twilight  of  the  evening  insensibly  disengages 
his  attention  from  objects  of  sight,  and  the  darkness  of 
night  finds  him  again  in  repose.  He  soon  walks  forth 
under  the  heavens.  He  notices,  that  when  darkness 
gives  way  to  light,  the  sun  becomes  visible  in  the  east ; 
and  that  when  the  sun  has  passed  through  the  heavens, 
he  disappears  in  the  west,  and  light  gradually  yields  to 
darkness.  At  the  same  time  that  these  changes  are  no- 
ticed by  the  eye,  he  feels  that  warmth  or  heat  increases 
and  decreases,  much  in  the  same  manner,  and  in  the  same 
degree,  that  light  does  ;  and  that  at  the  same  time  that 
darkness  steals  one  object  after  another  from  his  sight, 
a  sensation  of  cold  pervades  his  frame.  He  soon  comes 
to  this  conclusion,  that  the  sun  is  the  grand  dispenser 
of  heat  and  light ;  that  the  day  is  caused  by  his  pre- 
sence ;  and  that  the  coldness  and  darkness  of  night  are 
nothing  but  his  absence. 

2.  Besides  the  changes  of  heat  and  cold  which  a 
eiu^le  day  exhibits,  he  will  pass  but  a  small  part  of  the 


Z  INTRODUCTION. 

ordinary  age  of  man,  before  he  becomes  sensible  of 
other  changes.  He  observes  a  long  succession  of  days 
and  nights,  during  which  the  atmosphere  is  warm  and 
<:omfortable  to  himself  and  all  other  animals,  and  the 
earth  puts  forth  her  thousand  forms  of  vegetable  life. 
By  degrees  the  atmosphere  is  divested  of  its  heat,  the 
vegetable  kingdom  is  stript  of  its  foliage,  and  cold  and 
spow  succeed  agreeable  temperature  and  verdure.  Af- 
ter some  length  of  time,  he  beholds  the  earth  again 
renovated,  and  nature  again  rejoicing  in  genial  warmth. 
During  these  changes,  the  sun  appears  to  move  north- 
ward., and  southivard.  By  witnessing  a  few  of  these 
changes,  he  understands  what  is  meant  by  the  seasons. 
Summer  and  Winter,  Sjrring  and  Autumn, 

3.  When  the  sun  has  ajyparentJy  retired  from  crea- 
tion, night  presents  its  countless  multitude  of  shining 
bodies.  The  most  careless  observer  cannot  long  with- 
hold attention  to  the  ever  varying  phases  of  the  moon. 
At  one  time,  it  is  seen  just  after  sunset,  like  half  a  ring. 
Gradually  this  ring  fills  up,  or  thickens,  till  in  about  a 
week,  it  becomes  a  semicircular  surface.  It  continues 
to  increase,  till  the  surface  becomes  perfectly  circular. 
It  then  decreases,  as  it  had  before  increased,  and  for  a 
short  time  is  invisible  ;  when  it  ap_pears  again  as  a  part 
of  a  ring. 

4.  From  the  moon  the  eye  glances  to  those  bodies, 
which  are  known  to  youth  as  stars.  The  observations 
of  a  short  period  are  sufficient  to  establish  the  appa-  - 
rent  truth,  that  most  of  them  are  fixed  and  stationary, 
always  preserving  the  same  apparent  distance  and  di- 
rection from  each  other  5  but  that  some  of  them  are 


INTRODUCTION.  \S 

wandering,  continually  changing  their  position  with 
regard  to  other  bodies  apparently  in  their  neighbour- 
hood. The  former  are  considered  as  stars,  or  Jbced 
stars ;  the  latter  are  planets.  Occasionally  a  stranger 
appears,  which  unlike  other  heavenly  bodies,  is  accom- 
panied by  a  train  or  tail  more  or  less  luminoui,  and 
which,  in  a  longer  or  shorter  period,  becomes  again 
invisible.     These  are  comets, 

5.  These  observations,  which  are  now  familiar  to 
the  mind  in  youth,  not  to  say  in  childhood,  show  that 
all  the  heavenly  bodies,  except  the  stars,  and  perhaps  the 
sun,  are  in  motion.  From  this  single  fact  result  all  the 
changes  in  nature.  To  produce  day  and  night,  either 
the  sun  goes  round  the  earth,  or  the  earth  turns  so  as  to 
present  different  parts  to  the  sun,  in  a  day.  To  pro- 
duce the  seasons,  either  the  sun  8  ^tually  moves  north- 
ward and  southward,  or  the  earth  has  such  a  motion  as 
to  present  the  northern  part  to  the  sui.  in  one  season, 
and  the  southern  part  m  another.  The  moon,  planets, 
and  comets,  by  changing  their  position  with  regard  to 
the  stars,  and  also  to  each  other,  must  obviously  have 
a  motion.  In  manhood,  the  mind  inquires  into  the 
nature  and  motions  of  the  heavenly  bodies ;  observes 
the  various  phenomena,  which  they  present ;  and,  as 
far  as  it  is  able,  educes  the  laws,  by  which  their  mo- 
tions are  regulated.  The  Science,  which  explains  these 
particulars,  is  called  Astronomy.  It  is  divided  into 
descriptive  Astronomy,  and  physical  Astronomy.  The  first 
includes  an  account  of  the  phenomena  of  the  heavenly 
bodies;   the  last  explains  the  theory  of  their  motions. 


BOOK  I. 
DESCRIPTIVE    ASTRONOMY, 

CHAP.  I. 

Sect.  1.     Of  the.  Solar  System  in  general. 

6.  The  true  Solar  system,  or,  as  it  is  sometimes 
called,  the  Cojjernican  system,  consists  jof  the  sun  and 
an  unknown  number  of  bodies  opaque,  like  our  earth.; 
all  of  which  bodies  revolve  round  the  sun,  and  sonle 
of  which  at  the  same  time  revolve  round  others. 
(Those  which  revolve  round  the  sun  only,  are  called 
primary  planets  and  comets.  Those  which  revolve  round 
a  primary  planet,  at  the  same  time  ihat  they  are  re- 
volving round  the  sun,  are  called  secondary  planets 
moons  or  satellites^:'  The  number  of  primary  planets  is 
1 1 .  \iz,( Mercury,  Venus,  the  Earth,  Mars,  Vesta,  Juno, 
Pallas,  Ceres,  Jupiter,  Saturn,  and  Uranus^  The  num- 
ber of  the  secondary  planets,  moons  of  satellites,  is 
18,;  the  Earth  has  1,  Jupiter  has  4,  Saturn  has  7,  and 
Uranus  has  6.     The  number  of  the  comet?  is  unknown. 

7.  The  sun  is  in  the  centre  of  the  system.  (See 
Frontispiece.)  The  primary  planets  more  round  him 
in  the  order  above  named,  at  different  distances  and  in 
different  times,  from  west  to  east.  (It  n*  to  be  noticed^ 
that  in  all  the  figures  referred  to  m  this  tr  latise,  the  upper 
part  is  south,  the  lower  part  north;  the  light  hand  west j 
ond  the  left  hand  east.)  They  are  often  distinguished, 
especially   in   almanacs,    by   the    signs    used    in    tlie 


Of  the  Solar  System  in  general,  5 

Frontispiece,  viz.  ^  Mercury,  $  Venus,  ©  Earth, 
%  Mars,  §  Vesta,  ^  Juno,  $  Pallas,  ^  Ceres,  J/  Jupi- 
ter, 12  Saturn,  13^  Uranus.  The  path,  which  a  heavenly 
body  describes  in  its  revolution,  is  called  its  orhit. 
The  secondary  planets  generally  move  round  then*  pri- 
maries/in  the  same,  direction,  in  which  the  primaries 
move  round  the  sun^'  (The  small  circle  round  the  earth 
represents  the  moon'^s  oi^hit.  Each  of  the  satellites  of  Ju- 
piter, of  Saturn,  and  of  Uranus,  describes  an  orhit  round 
its  primary,  similar  to  that  of  the  moon  round  the  earth.) 
Comets  move  in  all  directions.  A  part  of  a  comet's  or- 
bit is  represented  in  the  Frontispiece. 

8.  Though  in  the  Frontispiece  the  orbits  of  the 
planets  are  circles,  yet  this  is  not  their  true  form.  All 
the  revolving  bodies  in  the  solar  system  move  in  orbits 
oval  or  elliptical,  (PI.  I,  fig.  2.)  JIBDE  is  an  ellipse,'^ 
and  represents  the  orbit  of  a  planet,  say  of  the  earth. 
The  points  S,  s,  are  called  foci  of  the  ellipse.  (The 
sun,  instead  of  being  in  the  centre  C,  is  in  one  of  the 
foci,  as  Sj  In  like  manner,  when  a  secondary  planet 
revolves  round  a  primary,  the  primary  is  not  in  the 
centre  of  its  orbit,  but  in  one  of  its/oa.  (That  focus  of 
an  orbit,  in  which  the  sun  or  a  primary  planet  is^  is 
called  the  loicer  focus  ;  /'and  the  other  is  called  the  ujpper 
focusy  (When  any  bo^y,  revolving  round  the  suri,  is 
nearest  to  him,  as  at  A,  it  is  said  to  be  in  its  perihelion; 
and  when  it  is  most  distant,  as  at  B,  it  is  said  to  be  in 
its  aphelion.  When  the  moon  is  nearest  the  earthy  it  is 
said  to  be  in  perigee  ;  when  at  its  greatest  distance,  it  is 
said  to  be  in  apogee.     The  line  SD  is  the  mean  dis- 

*  To  describe  an  Ellipse,  pin  down  the  ends  of  a  string  upon  a  table 
or  piece  of  paper,  at  any  two  places,  as  S,  s.  The  string  should  not 
be  drawn,  but  be  left  slack.  Then  with  a  pencil  stretch  the  string  as 
far  as  it  will  extend  in  every  direction,  and  the  point  of  the  pencil  will 
describe  an  ellipse.  The  points  5,  5,  where  the  string  is  fastened,  are 
the  foci.  The  ellipse  will  always  be  more  or  less  eccentric  in  propor- 
tion as  the  string  is  drawn  more  or  less  tightly. 


6  Of  the  Solar  System  in  general. 

tance  of  the  orbit  from   the  lower  focus ;    SC   is  its 

eccentricity. 

Though  the  orbits  of  the  planets  in  the  frontispiece  are  circles,  yet 
they  are  not  concentric,  that  is,  Iiave  not  the  same  centre.  The  cen- 
tre of  each  orbit  is  placed  out  of  the  centre  of  the  sun  at  a  distance 
equal  to  the  eccentricity  of  its  true  orbit.  Each  planet  is  placed  in  its 
aphelion. 

The  relative  distances  of  the  primary  planets  from  the  sun  could 
not  be  well  preserved  in  this  figure,  but  are  represented  in  the  margin. 

9.  The  sun  ajid  all  the  planets,  primary  and  seconda- 
ry, are  globular,  though  not  perfect  globes.  This  is 
known  of  all,  except  the  earth, (by  their  always  appear- 
ing nearly  round  to  the  naked  eye,  or  through  a  tele- 
scope.: It  is  known  of  the  earth,  by  its  shadow  on  the 
moon  in  an  eclipse,  which  is  always  circular!  PI.  I,  fig. 
4,  represents  the  relative  magnitudes  of  seven  of  the 
primary  planets  and  the  moon,  together  with  the  ring 
of  Saturn,  which  will  be  described  hereafter.  The  di- 
ameter of  the  sun  in  relation  to  that  of  the  planets,  as 
here  represented,  is  about  one  foot.  The  relative  sizes 
of  the  same  planets  are  represented  on  the  accompany- 
ing WQod-cut. 

10.(  The  sun  and  the  primary  and  secondary  planets, 
as  far  as  astronomers  have  means  and  opportunity  of 
ascertaining,  turn  on  imaginary  lines  passing  through 
their  centres,  which  are  called  axes)  The  time,  in 
which  the  heavenly  bodies  turn  on  tlieir  axes,  is  vari- 
ous ;  but  generally  the  largest  turn  quickest.  A  mire 
passing  through  the  centre  of  an  apple  properly  represents 
the  axis  of  a  planet.  Tlie  extremities  of  an  axis  are  called 
(poles.) 

ii.'lf  the  earth  were  seen  from  the  sun,  (PI.  J,  fig 
1,)  it  would  appear  to  describe  a  circle  among  the 
stars,  while  it  revolves  in  its  orbit.  For  while  it  is 
passing  from  A  to  jB,  it  would  be  seen  to  move  among 
the  stars  from  a  to  h.     And  in  like  manner  tlirough  *ts 


RELATIVE  SIZES  OF  THE  PLANETS. 


I 


Of  the  Solar  System  in  general.  7 

whole  orbit.  While  the  earth,  viewed  from  the  sun, 
w^ould  describe  this  circle  among  the  stars,  the  sun,  to 
us  on  earth,  appears  to  describe  precisely  the  same 
circle,  only  beginning  at  the  opposite  point.  For  while 
the  earth  actually  moves  from  A  to  J3,  the  sun  appears 
to  move  from  c  to  d ;  and  while  the  earth  moves  from 
B  to  C,  the  sun  appears  to  move  from  d  to  a,  and  so  on. 
This  path  or  circle,  which  the  earth  describes  as  seen 
from  the  sun,  and  which  the  sun  appears  to  us  to 
describe,  is  called  the  ecliptic  ;  and  a  plane,  passing 
through  this  circle,  is  called  the  plane  of  th^  ecliptic. 
(The  surface  of  the  paper  on  which  the  f^ure  is  drawn, 
properly  represents  a  plane.)  The  ecliptic,  and  in 
fact  all  circles,  whether  great  or  small,  are  divicjed 
into  360  degrees  (marked  °),  and  each  degree  into' GO 
minutes,  (marked  ^),  and  each  minute  into  60.  seconds, 
(marked  ^^),  and  so  on  into  smaller  divisio^is.  The 
ecliptic  has  a:  other  division  into  12  signs;  containing  of 
course  '30^  each.  The  division  into  signs,  and  the 
names  of  the  signs  are  given  in  the  fig'ire,  beginning 
with  Aries,  and  reckoning  through  Taurus,  Gemini,  &c. 
Instead  of  the  names  of  the  signs,  the  characters  prefixed 
to  them  in  the  figure,  are  often  used.  These  characters 
are  placed  in  the  ecliptic  in  the  Frontispiece  :  by 
which  it  may  be  readily  seen  in  what  sign,  and  nearly  in 
what  part  of  a  sign,  is  the  aphelion  of  each  planet.  The 
English  names  of  the  signs,  in  order,  are  the  Ram,  the 
Bull,  the  Twins,  the  Crab,  the  Lion,  the  Virgin,  the 
Scales,  the  Scorpion,  the  Archer,  the  Goat^  the  Water- 
Bearer,  the  Fishes. 

The  instriicter  should  explain  degrees  to  the  pupil ;  show  him,  that 
the^  are  not  of  any  absolute  determinate  length,  but  vary  as  the  circle 
is  greater  or  smaller.  This  may  be  readily  done  by  drawing  two  cr 
three  concentric  circles,  and  a  few  lines  from  the  centre  to  the  outer- 
most circle 

12.  But  the  other  primary  planets,  when  seen  from 


8  '  Of  the  Sun. 

the  sun,  do  not  describe  exactly  the  same  circle  among 
the  stars,  that  the  earth  does  ;  but  are  sometimes  on  one 
side  of  the  ecliptic,  and  sometimes  on  the  other.  But 
none  of  them,  except  Juno,  Pallas,  £.nd  Ceres,  are  ever 
farther  distant  from  the  ecliptic  than  8^.  So  that  within 
a  zone  or  belt  of  IG^,  (S^  on  each  side  of  the  ecliptic,) 
the  planets,  except  those  just  named,  are  always  to  be 
founds  This  zone  is  called  the  Zodiac.  It  is  repre- 
sented by  the  dark  belt  interspersed  with  stars,  in  the 
figure.  The  inner  half  represents  the  part  beyond  the 
ecliptic  ;  the  outer  half,  the  part  on  this  side.  The 
points,  where  the  orbit  of  any  heavenly  body  cut^'  the 
plane  of  the  ecliptic^  are  called  the  nodes  of  that  body. 
The  point,  where  the  body  passes  from  ^he  north  side 
of  the  plane  of  the  ecliptic  to  the  southj  is  called  its 
descending  node ;  w^here  it  passes  from  the  south  to  the 
north,  its  ascending  node. 

In  order  that  what  has  been  said  may  be  well  understood,  it  may  be 
necessary  for  the  pupil  to  go  over  it  again  and  again.  Nothing  should 
^^  *  ssed  over  without  being  understood.  Instructers  should  explain 
and  illustrate  what  is  obscure,  and  in  many  cases  necessarily  so.  A 
familiar  illustration  will  give  a  pupil  a  better  idea  of  such  things  as 
axis,  plane,  degree^  focus,  and  many  others,  than  can  be  done  in  a 
dozen  pages. 


Sect.  2.     Of  the  Sun. 

13.  The  sun  is  the  centre  of  the  solar  system,  dis- 
pensing heat  and  light  to  all  the  various  bodies,  which 
continually  move  round  him.  Like  the  Centre  of  the 
universe,  the  sun  is  constantly  imparting  of  its  own  to 
recipient  subjects.  All  the  bodies  in  our  system,  which 
revolve  round  Jiim?  impart  no  rays  of  their  own,  but 
are  seen  by  his  light  reflected.  In  like  manner  in  uni- 
versal nature,  we  see  reflected,  the  love  and  wisdom  of 
the  Lord.     The  different  distances  of  the  planets  from 


Of  the  Sun.  9 

the  sun  occasion 'a  reception  of  different  degrees  of 
heat  and  light.  These  are  received  according  to  the 
square  of  the  distance  of  the  planet  from  the  sun ;  that 
is,  they  decrease  as  the  square  of  the  distance  increases. 
Thus,  if  the  distance  of  one  planet  from  the  sun  be  1, 
and  the  distance  of  another  be  2,  and  of  a  third  be  3 
the  heat  and  light  received  at  the  first  is  1  X  1  =  1,  at 
the  second  2x2  =  4  times  less,  or  J,  at  the  third 
3x3  =  9  nine  times  less,  or  ^. 

14.  The  truth  of  this  rule  admits  of  familiar  proof. 
(PI.  II,  fig.  1.)  Let  ^  be  a  lamp,  ^J^"*  a  square  hole 
cut  through  a  piece  of  pasteboard,  placed  at  the  dis- 
tance of  1  foot  from  the  lamp.  Let  the  heat  and  light, 
which  pass  through  the  hole  BF,  fall  upon  a  surface 
CO,  at  the  distance  of  2  feet  from  the  lamp  ;  it  will  be 
seen,  that  the  surface  CO  is  4  times  greater  than  the 
hole  or  surface  BF ;  consequently,  the  heat  and  light 
at  any  point  in  CO,  is  4  times  less,  than  at  a  point  in 
BF.  But  if  there  be  a  surface  DS,  at  the  distance  of 
3  feet,  instead  of  CO,  it  will  be  found,  that  the  heat 
and  light  passing  through  BF  is  diffused  over  a  surface 
9  times  greater  than  BF ;  consequently,  the  heat  and 
light  at  any  point  in  DS  is  nine  times  less,  than  at  a 
point  in  BJF,  Thus,  as  the  square  of  the  distance  in- 
creases, heat  and  light  decrease. 

15.  The  sun  does  not  always  exhibit  the  same  ap- 
pearance. Dark  spots  are  often  seen  on  his  disk;  and 
sometimes,  spots  brighter  than  the  rest  of  his  surface. 
They  appear  to  cross  the  disk  from  east  to  west ;  are 
alternately  visible  and  invisible  for  .the  same  length  of 
time.  Whence  it  is  certain,  that  the  sun  turns  on  his 
own  axis  from  west  to  east.  The  time  of  his  rotation  is 
little  more  than  25  days.  The  cause  of  these  spots, 
which  often  change  their  size  and  figure,  is  not  known. 

16.  The  Zodiacal  light  is  a  singular  phenomenon, 
accompanying  the  sun.     It  is  a  faint  light  which  often 

2* 


10  Of  Mercury. 

appears  to  stream  up  fiom  the  sun  a  little  after  sunset 
and  before  sunrise.  It  appears  nearly  in  the  form  of  a 
cone,  its  sides  being  somewhat  curved,  and  generally 
but  ill  defined.  It  extends  often  from  50^  to  100^  in 
the  heavens,  and  always  nearly  in  the  direction  of  the 
plane  of  the  ecliptic.  It  is  most  distinct  about  the  be- 
ginning of  March  ;  but  is  constantly  visible  in  the  tor- 
rid zone.    The  cause  of  this  phenomenon  is  not  known. 

In  Almanacks,  the  sun  is  usually  represented  by  a  small  circle,  with 
the  face  of  a  man  in  it. 


Sect.  3.      Of  Mercury, 

17.  Proceeding  from  the  sun,  the  grand  centre  of  the 
system,  the  first  planet  is  Mercury*  It  revolves  round 
the  sun  at  nearly  the  mean  distance  of  37  millions  of 
miles,  and  completes  its  revolution  in  about  3  months. 
The  time,  in  which  it  turns  on  its  axis,  is  about  24  hours. 
It  emits  a  brilliant  white  light ;  but  because  it  is  near 
the  sun,  and  consequently  seldom  out  of  twilight,  it  is 
not  often  noticed.  Its  greatest  apparent  distance  from 
the  sun,  or  its  greatest  elongation^  is  never  more  than 
28'^.  When  viewed  through  a  good  telescope,  it  ex- 
hibits all  the  diflferent  appearances  or  phases,  which  the 
moon  does,  and  they  are  to  be  accounted  for  in  the 
same  manner.     Of  this  we  shall  treat  hereafter. 

18.  The  distance  of  Mercury  from  the  sun  is  to  that 
of  the  earth  nearly  as  3  to  8.  Therefore  the  degree  of 
heat  and  light  at  Mercury  is  to  that  at  the  Earth,  nearly 
as  (8  X  8)  64  to  (3  X  3)  9  ;  which  is  very  nearly  as  7 
to  1.  Consequently,  at  Mercury,  heat  and  light  are  7 
times  greater  than  with  us.  Water  would  there  fly  off 
in  steam  and  vapour. 


TELESCOPIC  APPEARANCES  OF  VENUS. 


Of  Venus.  21 

Sect.  4.     Of  Venus. 

19  Next  to  Mercury,  in  the  Solar  system,  is  Venus. 
This  planet  revolves  round  the  sun  at  the  mean  dis- 
tance of  68  millions  of  miles.  It  completes  its  revolu- 
tion in  about  7^  months;  an&  turns  on  its  axis  in  little 
less  than  24  hours.  The  light  reflected  by  this  planet  is 
very  brilliant,  and  often  renders  it  visible  to  the  naked 
eye.  in  the  day  time.;    Its  greatest  elongation  is  about 

<  47^}  It  exhibits  phases  similar  to  those  of  Mercury  and 
the  moon.  Spots  are  sometimes  seen  on  its  surface  ; 
the  appearances  of  which,  and  its  phases,  are  exhibited 
in  the  annexed  wood-cut.     Heat  and  light  at  Venus  are 

(nearly  double  what  they  are  at  the  earth. 

20.  This  planet  is  brightest,  when  she  is  about  40*^  * 
distant  from  the  sun  ;  and  then  only  about  J  part  of  her 
disk  is  illuminated.  ^  Her  brightness  in  this  position  is 
surprising.  Her  lustre  far  exceeds  that  of  the  moon, 
at  the  same  apparent  distance  from  the  sun.  For 
though,  on  account  of  her  appar  t  magnitude,  the 
moon  reflocis  more  light  to  us  than  Venus  does,  yet  this 
light  is  incomparably  more  dull,  and  nas  none  of  the  life 
and  briskness  which  attend  the  beanis  of  Venus.  This 
difference  arises  probably  from  the  circumstance  of 
(Venus  having  a  very  dense  atmosphere,  while  the  moon 
has  a  very  rare  one^ 

21.' Mercury  and  Venus  are  called  interior  plarets, 
because  they  are  nearer  the  sun  than  the  earth'  is  ;  w  hile 
those  that  are  farther  from  the  sun  than  the  earth  is 
are  called  exterior.'^     They  exhibit  some  peculiarities, 

*  In  most  books  on  astronomy,  what  are  here  called  interior  pla- 
nets, are  styled  inferior;  and  what  are  here  called  exterior ,  are  there 
denominated  superior.  But  why  this  distinction  of  superior  and  infe- 
rior was  ever  made,  it  is  difficult  to  see.  In  what  proper  sense  can 
the  word  superior  be  applied  to  Mars  in  comparison  of  the  Earth  or 
Venus  ?  Since  every  natural  blessing  of  existence  is  derived  from  the 
oeat  and  light  of  the  sun,  we  should  suppose  that  planets  would  be 


12  Of  Venus. 

arising  from  their  situation  ;  but  as  Mercury  is  seldom 
seen,  those  of  Venus  only  will  be  noticed.  During 
a  part  of  its  revolution,  Venus  rises  and  sets  before  the 
sun  ;  it  is  then  called  ^morning  star.  During  another 
part  of  its  revolution,  it  rises  and  sets  after  the  sun  ;  it 
is  then  called  evening  star,^  (PL  II.  fig.  2.)  Let  S  be 
the  sun,  BDEC  the  orbit  of  Venus,  A  the  earth,  AL  a 
part  of  its  orbit,  while  Venus  is  moving  from  C,  (which 
point  is  called  its  superior  conjunction)  through  B  to  D, 
it  will  appear  to  the  inhabitants  of  the  earth  at  A  to  be 
above,  or  eastward  of  the  sun  ;  it  will  consequently  be 
visible  after  the  sun  has  set.  But  while  passing  from  Z>, 
(which  point  is  called  its  inferior  conjunction,)  through 
IE  to  C,  it  will  appear  below  or  w^estward  of  the  sun, 
and  will  consequently  set  before  the  sun. 

22.  If  the  earth  were  stationary  at  A^  it  is  obvious 
that  Venus  would  be  above  the  sun,  and  be  evening  star 
in  half  its  orbit ;  and  be  below^  the  sun,  and  be  morning 
star  in  the  other  half.  But  because  the  earth  is  in  mo- 
tion, Venus  is  above  and  below  the  sun  alternately,  in 
much  more  of  its  orbit.  For  let  Venus  emerge  above 
the  sun  at  C,  when  the  earth  is  at  Jl ;  while  it  is  coming 
through  B  to  jD,  the  earth  passes  from  A  to  F ;  conse- 
quently Venus  must  pass  from  D  to  d,  before  it  is  seen 
below  the  sun.  So  while  Venus  moves  from  d  to  a?, 
(half  its  orbit,)  the  earth  has  come  to  o;  consequently 
Venus  must  move  on  from  x  to  v  before  it  emerges  again 
above  the  sun.  This  effect  is  very  much  greater  than 
is  represented  on  the  figure.      For  while  Venus  passes 

tuperior  according  to  the  degree  of  heat  and  light  which  they  receiv- 
ed ;  that  is,  according  to  their  proximity  to  the  sun.  This  distinction 
of  interior  and  exterior  is  not  new,  though  but  few  have  adopted  it; 
but  being,  (as  I  conceive,)  much  the  most  appropriate,  I  feel  desirous 
of  having  it  adopted. 

*  The  Ancients  called  the  morning  star,  Phosphorus ;  and  the 
evening  star,  Hesperus.  These  names  are  now  often  used_,  especially 
in  poetry. 


Of  the  Earth  and  Moon,  13 

from  C  to  Z),  half  its  orbit,  the  earth,  instead  of  passing 
through  the  small  portion  JlF^  has  passed  through  nearly 
J  of  her  orbit  ]  through  which,  and  considerably  more, 
(because  the  earth's  motion  is  constant,)  Venus  must 
pass  before  she  is  seen  below  the  sun.  It  is  found  that 
Venus  is  morning  and  evening  star  alternately,  during 
fabout  290  days^  a  period,  considerably  exceeding  a 
complete  revolution  of  that  planet  in  her  orbit. 

SECT.  5. 

Art.   1.     Of  the  Earth. 

23.  The  planet  next  to  Venus  in  the  solar  system, 
is  the  earth,  which  we  inhabit.  It  revolves  about  the 
sun  at  the  mean  distance  of  53  millions  of  miles.  It 
completes  this  revolution  in  a  year,  and  turns  on  its  axis 
in  a  day,  or  twenty-four  hours.  The  consideration  of 
the  figure  of  tiie  earth  will  be  resumed  when  we  come 
to  treat  of  physical  Astronomy ;  and  the  other  pheno- 
mena relating  to  this  planet  will  be  continued  in  Chap. 
II.  and  III. 

Art.  2.     Of  the  Moon. 

24.  The  moon  is  a  secondary  planet,  revolving  round 
the  earth  in  about  29J  days,  and  is  carried  with  the 
earth  round  the  sun  once  a  year.  Its  distance  from  the 
earth  is  about  240,000  miles.  It  turns  on  its  axis  in 
precisely  the  same  time  that  it  performs  its  revolution 
round  the  earth. 

25.  The  most  obvious  fact  relating  to  the  moon,  is, 
that  her  disk  is  constantly  changing  its  appearance  , 
sometimes  only  a  semicircular  edge  is  illuminated, 
while  the  rest  is  dark  ;  and  at  another  time,  the  ^yhole 
surface  appears  resplendent.     The  first  appearance  is 


14  Of  the  Moon. 

called  the  new  moon,  and  is  exhibited  when  the  sun 
and  moon  appear  near  each  other  ;  that  is,  in  the  same 
region  of  the  heavens.  The  second  is  called  the  fuU 
moon,  and  is  exhibited  when  the  sun  and  moon  appear 
most  distant ;  that  is,  in  opposite  regions  of  the  heavens. 
(When  the  moon  is  in  conjunction  with  the  sun,  that  is, 
passes  by  him,  it  is  said  to  change ;  and  when  it  is  in 
opposition  to  the  sun,  that  is,  when  the  sun  is  in  one 
part  of  the  heavens,  as  west,  and  the  moon  in  the  oppo- 
site part,  as  east,  the  moon  is  said  to  fulL 

26.  The  different  phases  of  the  moon  are  easily 
accounted  for.  In  PI.  II,  fig.  3,  let  S  be  the  sun,  JG 
the  earth,  and  ABCD  the  moon  in  different  parts  of 
her  orbit.  When  the  moon  changes,  as  at  e/2,  its  dark 
side  will  be  towards  the  earth,  its  illuminated  part  being 
always  towards  the  sun.  Hence  the  moon  will  appear 
to  us  as  represented  at  «,  if  it  be  seen  at  all.  '  But  when 
she  has  advanced  in  her  orbit,  and  come  to  JS,  a  small 
part  of  her  illuminated  side  comes  in  sight,  and  she  ap- 
pears as  represented  at  6,  a  new  moon,  and  is  said  to 
be  horned.  When  she  has  come  to  C,  one  half  her 
illuminated  side  is  visible,  and  she  appears  as  at  c.  At 
C  and  in  the  opposite  point  of  her  orbit,  the  moon  is 
said  to  be  in  quadrature.  At  D  her  appearance  is  as 
represented  at  r7,  and  she  is  said  to  be  gibbous.  At  E 
all  her  illuminated  side  is  towards  us,  and  we  have  a 
full  moon.  During  the  otl  er  half  of  her  revolution,  less 
and  less  of  her  illuminated  side  is  seen  till  it  again  be- 
comes invisible  at  A. 

The  following  signs  are  used  in  our  common  almanacs  to  denote 
the  different  positions  and  phases  of  the  moon.  )  or  D  denotes  the 
moon  in  the  ^r5i  quadrature,  that  is,  the  quadrature  between  change 
and  full.  C  or  d  denotes  the  moon  in  the  last  quadrature,  that  is,  the 
quadrature  between  full  and  change.  Q  denotes  new  moon.  %  de- 
notes full  moon. 

27.  The   earth,  seen  from  the  moon,  exhibits  pre- 
cisely  the  same  phases  that  the  moon  does  to  us ;  only 


Of  the  Moon.  15 

in  an  opposite  order.  When  the  moon  is  full  to  us,  the 
earth  will  be  dark  to  the  inhabitants  of  the  nibon ;  and 
when  the  moon  to  us  is  dark,  the  earth  to  them  is  full. 
The  earth  appears  to  them  about  13  times  larger  than 
the  moon  does  to  us.  But  as  the  moon  turns  on  its 
axis  in  the  same  time  that  it  goes  round  the  earth,  she 
always  exhibits  the  same  side  to  us  ^  consequently  f  we 
never  see  one  half  of  the  moon's  surface,  and  the  earth 
is  never  seen  by  that  portion  of  the  moon's  inhabitants 
who  dwell  there. 

28.  When  viewed  through  a  telescope,  the  surface 
of  the  moon  appears  wonderfully  diversified.  Large 
dark  spots,  which  are  excavations  or  valleys,  are  visible 
to  the  eye  ;  also  some,  which  are  even  more  lucid  than 
the  general  surface;  These  are  ascertained  to  be  moun- 
tains, by  the  shadows  which  they  cast.  Maps  of  the 
moon's  surface  have  been  drawn ;  on  which  most  of 
these  valleys  and  mountains  are  delineated,  and  names 
are  given  to  them.  /Some  of  these  excavations  are  thought 
to  be  4  miles  deep  and  40  wide.    A  high  ridge  generally 

C surrounds  them,  and  often  a  mountain  rises  in  the  centre. 
These  immense  depressions  probably  very  much  resem- 
ble what  would  be  the  appearance  of  the  earth  at  the 
moon,  were  all  the  seas  and  lakes  dried  up.  Some  of 
the  mountains  are  supposed  to  be  volcanic. 

Dr.  Brewster,  speaking  of  the  Moon,  says,  *'  Her  mountainous  sce- 
nery bears  a  stronger  resemblance  to  the  towering  sublimity,  and  the 
terrific  ruggedness  of  Alpine  regions,  than  to  the  tamer  iiiequalities 
of  less  elevated  countries.  Huge  masses  of  rock  rise  at  once  from 
the  plains,  and  raise  their  peaked  summits  to  an  immense  height  in 
the  air,  while  projecting  crags  spring  from  their  rugged  flanks,  and 
threatening  the  valleys  below,  seem  to  bid  defiance  to  the  laws  of 
gravitation.  Around  the  base  of  these  frightful  eminences,  are  strew- 
ed numerous  loose  and  unconnected  fragments,  which  time  seems  to 
have  detached  from  their  parent  mass  ;  and  when  we  examine  the 
rents  and  ravines  which  accompany  the  over-hanging  cliffs,  we  ex- 
pect every  moment  that  they  are  to  be  torn  from  their  base,  and  that 
the  process  of  destructive  separation  which  we  had  only  contemplat- 
ed in  its  effects,  is  about  to  be  exhibited  before  us  in  tremendous  real- 


16  Of  Mais 

hy.  The  mountains,  called  the  Apennines,  which  traverse  a  portion 
of  the  moon's  disk  from  north-east  to  south-west,  rise  with  a  precipi 
tons  and  craggy  front  from  the  level  of  the  Mare  Imbrium.  In  some 
places,  their  perpendicular  elevation  is  above  four  miles  ;  and  though 
tiiey  often  descend  to  a  much  lower  level,  they  present  an  inaccessi- 
ble barrier  to  tli^  north-east,  while  on  the  south-west  they  sink  in 
gentle  declivity  to  the  plains. 

"  The  analogy  between  the  surface  of  the  earth  and  the  moon  fails 
in  a  still  more  remarkable  degree,  when  we  examine  \\  e  circular 
cavities  which  appear  on  every  part  of  her  disk.  Some  of  these  im 
mense  caverns  are  nearly  four  miles  deep  and  forty  miles  in  diame 
ter.  A  high  annular  ridge,  marked  with  lofty  peaks  and  little  cavi- 
ties generally  encircles  them  :  an  insulated  mountain  frequently  rises 
in  their  centre,  and  sometimes  they  contain  smaller  cavities  of  the 
Bame  nature  with  themselves.  These  hollows  are  most  numerous  in 
the  south-west  part  of  the  moon  ',  and  it  is  from  this  cause,  that  that 
portion  of  this  luminary  is  more  brilliant  than  any  other  part  of  her 
disk.  The  mountainous  ridges  which  encircle  the  cavities,  reflect  the 
greatest  quantity  of  light :  and  from  their  lying  in  every  possible  di- 
rection, they  appear,  near  the  time  of  the  full  moon,  like  a  number 
of  brilliant  radiations,  issuing  from  the  small  spot  called  Tycho. 

''  It  is  difficult  to  explain,  with  any  degree  of  probability,  the  for- 
mation of  these  immense  cavities  ;  but  we  cannot  help  thinking,  that 
our  earth  would  assume  the  same  figure,  if  all  the  seas  and  lakes  were 
removed  ;  and  it  is  therefore  probable,  that  the  lunar  cavities  are 
either  intended  for  the  reception  of  wat«r.  or  that  they  are  the  beds 
of  lakes  and  seas  which  have  formerly  existed  in  the  moon.  The 
circumstance  of  there  being  no  water  in  the  moon  is  a  strong  confir 
mation  of  this  tlieory." 


Sect.  6.     Of  Mars. 

29.  Next  to  the  earth  is  the  planet  Mars.  It  revolves 
m  its  orbit  in  little  less  than^wo  years,  at  the  distance 
of'  144  millions  of  miles  from  the  sun  ^  and  turns  on  its 
axis  in  little  less  than  25  hours'.  The  light  reflected 
by  Mars  is  remarkably  red.  Spots  and  sometimes  belts 
have  been  seen  on  the  disk  of  this  planet,  some  of  which 
are  permanent,  and  others  variable.  Some  of  the  most 
remarkable  appearances  of  this  kind,  as  they  are  seen 
through  a  telescope,  are  represented  in  the  annexed 
wood-cut.     These  variations  are  supposed  to  arise  from 


TELESCOPIC  APPEARANCES  OF  MARS. 


Of  Vesta,  Juno,  Pallas,  and  Ceres. 


17 


clouds  and  vapours  floating  in  the  atmosphere.     The 
degree  of  heat  and  hght  at  Mars  is  sometliing  less  than 
(one  half  what  we  enjoy .> 

Sect.  7.     Of  Vesta,  Juno,  Pallas,  and  Ceres. 

30.  Next  to  Mars  in  the  solar  system  is  Vesta.  It 
was  discoverec/^by  Dr.  Olbers^j  of  Bremen,  (March  29, 
1807)  Its  light  is  pure  and  white  ;  and  renders  the 
plarr^t  visible  to  the  naked  eye.  It  revolves  round  ihe 
^un  at  the  mean  distance  off. about. 223  millions  of  miles,) 

fin  about  3  years  and  8  months;     The  time  of  turning 
on  its  axis  is  not  known. 

31.  Juno,  the  planet  next  to  Vesta,  was  discovered 
byfMr.  Harding,' near  Bremen,  September  1,  1804.  Its 
cofour  IS  red,  and  its  atmosphere  appears  cloudy.  Its 
mean  distance  from  the  sun  is  (about  253  millions  of 
miles.  -"  Its  orbit  is  very  elliptical ;  so  that  its  greatest 
distance  from  the  sun  is  nearly  double  its  least  distance, 
and  the  time  of  passing  through  one  half  its  orbit  is 
about  double  the  time  of  passing  through  the  othei-^alf. 
It  completes  its  revolution  in  ^bout  4  years  and  4  months, 
andds  supposed  to  turn  on  its  axis  in  about  27  hours. 

32.  Pallas  was  discovered  by  {pr.  Olbers,'  March  28, 
1802.1  It  appears  to  have  a  dense  cloudy  atmosphere. 
It  revolves  round  tlie  sun  in  an  orbit  nearly  as  elliptical 
as  that  of  Juno,  in  about  4  years  and  7  months,  at  the 
meanmistance  of  263  millions  of  miles.\  The  time  of 
turning  on  its  axis  is  not  known^ 

33.  Ceres  was  discovered,  at  Palermo,  in  Sicily,  by 
Piazza,  January  1,  1801.  Its  mean  distance  from  the 
sun  is  about  the  same  as  that  of  Pallas  ;  but  its  orbit  is 
less  elliptical.  It  is  of  a  ruddy  colour.  (It  revolves  round 
the  sun  in  very  nearly  the  same  time  that  Pallas  does ; 
and,  what  is  very  remarkable,  its  orbit  intersects  that 

a 


18  Of  Jupiter. 

of  Pallas.  All  these  planets  undergo  various  changes 
in  appearance  and  size  ;  so  that  their  real  magnitude  is 
not  ascertained  with  any  certainty. 

These  four  planets  have  been  very  recently  discovered,  and  but  lit- 
tle is  known  of  them  as  yet.  They  are  certainly  very  small.  In  the 
Table  at  the  close  of  this  Chap.  t\\eiv  probable  size  is  given,  except 
that  uf\  esta.  It  is  a  remarkable  fact,  that  some  irregularities,  ob- 
served in  tlie  motions  of  the  old  phmets,  induced  some  astronomers  to 
suppose  that  a  planet  existed  between  the  orbits  of  Mars  and  Jupiter  ; 
a  supposition  that  arose  long  previous  to  the  discovery  of  the  four  new 
planets,  which  vvc  have- just  noticed.  The  opinion  has  been  advanc- 
ed, that  these  four  small  bodies  originally  composed  one  larger  one, 
which,  by  some  unknown  force  or  convulsion,  burst  asunder.  This 
opinion  is  maintained  with,  much  ingenuity  and  plausibility  by  Dr. 
Brewster  in  the  Iviinburgh  Encyclopedia,  .'Irt.  Astronomy.  Dr. 
Brewster  further  snppo&es,  that  the  bursting  of  this  planet  may  hav»-» 
occasioned  the  phenomena  of  the  meteoric  stones  ;  that  is,  stones 
which  have  fallen  on  the  earth  from  the  atmosphere. 


Sect.  8.      Of  Jupiter, 

34.  Jupiter  revolves  at  the  mean  distance  of  490  mil- 
lions of  miles  from  the  sun.  It  completes  its  revolution 
in  little  less  than  12  years,  and  turns  on  its  axis  in  the 
short  time  of  9  hours  and  56  minutes.  It  is  the  largest 
planet  yet  discovered  in  the  solar  system,  being  S9,G00 
miles  in  diameter.  It  reflects  a  beautiful  light,  and  is 
the  most  brilliant  of  the  planets,  except  Venus.  The 
degree  of  heat  and  light  at  Jupiter  is  about  25  times 
less  than  at  the  earth. 

35.  When  viewed  through  a  telescope,  Jupiter  ex- 
hibits an  appearance  some^shat  diflerent  from  any  of 
the  above  planets.  Generally  several  belts  or  bands  are 
distinctly  seen,  sometimes  extending  across  his  disk,  and 
sometimes  interrupted  and  broken.  These  belts  are 
variable  in  distance  and  position  as  well  as  number. 
Tiiey  are  generally  dark,  but  white  ones  have  been  seen. 
1  heir  appearances  through  a  telescope  are  represented 


Of  Jupiter,  1 9 

in  the  annexed  wocTd-cut.  'Both  bright  and  dark  spots 
have  been  seen  in  them  ;  some  of  which  revolve  faster 
than  others,  which  shows  that  they  cannot  be  permanent 
spots  on  the  body  of  the  planet. 

36.  Jupiter  is  accompanied  by  4  moons  or  satellites. 
These  moons  revolve  round  Jupiter  as  the  moon  does 
round  the  earth.  Their  revolutions  are  completed  in 
different  times  ;  the  shortest  being  less  than  2  days,  and 
the  longest  less  than  17  days.  These  satellites  often  pass 
behind  the  body  of  the  planet,  and  also  into  its  shadow, 
and  are  eclipsed.  These  eclipses  are  of  use  in  ascer- 
taining the  longitude  of  places  on  the  earth,  as  will  be 
shown  hereafter.  For  this  reason  astronomers  have 
taken  great  pains  to  calculate  the  precise  time  when 
they  take  place  at  I^ondon.  By  these  eclipses  it  is  also 
ascertained  that  light  is  about  8  minutes  coming  from 
the  sun  to  the  earth.  For  an  eclipse  of  one  of  these 
satellites  appears  to  us  to  take  place  16  minutes  sooner, 
when  the  earth  is  in  the  part  of  her  orbit  nearest  Jupi- 
ter, than  when  in  the  part  farthest  from  him.  Hence 
light  is  16^  in  crossing  the  earth's  orbit,  and  of  course 
8'  in  coming  from  the  sun.  The  satellite  nearest  to 
the  primary  is  reckoned  1st,  and  the  others,  2d,  3d,  &c. 
as  they  are  farther  from  the  primary.  The  lirst  satellite 
is  somewhat  less  than  the  2d,  and  the  2d  somewhat  less 
than  the  4th,  which  is  about  as  large  as  our  moon  ;  but 
the  3d  is  about  twice  the  size  of  our  moon. 

37.  On  account  of  the  immense  distance  of  this 
planet  from  the  sun,  and  also  from  Mercury,  Venus,  the 
Earth,  and  Mars,  observers  on  Jupiter,  with  our  eyes, 
could  never  see  either  of  the  above  named  planets,  for 
they  are  always  immersed  in  the  sun's  rays.  They 
would  direct  their  observations  to  planets  which  lie 
beyond ;  and  here  we  know  not  the  advantages  of  a 
position  on  Jupiter  over  one  on  the  earth.  For  we 
know  not  how  many  planets  belonging  to  our  system, 


20  Of  Saturn. 

within  or  beyond  the  orbit  of  Saturn  or  of  Uranus,  are 
distinctly  visible  at  Jupiter,  whose  feeble  Hght  for  ever 
precludes  their  discovery  by  us. 


Sect.  9.     Of  Saturn. 

38.  Saturn,  at  the  mean  distance  of  900  millions  of 
miles,  completes  a  revolution  round  the  sun  in  little 
less  than  30  years.  It  turns  on  its  axis  in  little  more 
than  10  hours.  The  light  reflected  by  this  planet  is 
less  brilliant  than  that  of  Jupiter.  The  degree  of  heat 
and  light  from  the  sun  at  Saturn  is  80  times  less  than 
at  the  earth. 

39.  Saturn  is  remarkably  distinguished^  from  all  the 
other  planets  in  the  solar  system.  l^^hen  viewed 
through  a  telescope,  it  appears  encompassed  by  a  large 
luminous  ring.j  This  ring,  in  fact,  consists  of  two,  one 
exactly  without  or  beyond  the  other.  They  are  en- 
tirely detached  from  each  other  and  from  the  body  of 
the  planet.  (They  are  represented  PI.  I,  fig.  4,  and  in 
the  wood-cut^  exhibiting  the  relative  sizes  of  the  planets.) 
They  cast  a  deep  shadow,  and  appear  even  brighter 
than  the  planet )  perhaps  because  they  are  above  the 
region  of  mists  and  clouds  in  his  atmosphere.  They 
turn  on  the  same  axis  with  the  planet,  and  in  nearly  the 
same  time.  Stars  are  sometimes  seen  between  the  rings, 
and  alsp  between  the  inner  ring  and  body  of  the  planet. 

40.  /The  surface  of  Saturn  is  sometimes  diversified 
like  that  of  Jupiter  with  spots  and  belts ;  which,  like 
those,  often  vary^^  Saturn  has  7  satellites,  revolving  at 
different  distances,  and  in  various  times,  from  little  less 
than  1  day  to  nearly  80.  The  nearest  is  reckoned  7th, 
the  next  Gth,  the  others  1st,  2d,  &c.  in  order  outward. 
The  reason  is,  that  the  7th  and  Gth  are  of  recent  dis- 
covery 'j  the  others  have  been  long  known. 


TELESCOPIC  APPEARANCES  OF  JUPITER. 


Of  Uranus.  21 

Sect.   10.      Of  Uranus. 

41  The  planet  Uranus  was  discovered  by  Dr.  Her- 
schel  on  the  13th  March,  1781.  Before  that  time,  it  had 
been  seen  by  several  astronomers.  It  was  considered  a 
small  star,  and  was  introduced  as  such  into  several  ca- 
talogues of  the  stars.  But  Herschel  first  discovered  it 
to  be  a  planet,  fits  distance  from  the  sun  is  about  ISOO 
millions  of  miles.  The  time  of  performing  a  revolution 
is  about  84  years.  It  is  not  known  in  what  time  it  turns 
on  its  axis.  Heat  and  light  at  Uranus  are  about  360 
times  less  than  with  us.i  Uranus  is  scarcely  visible  to 
the  naked  eye. 

42.  This  planet  is  attended  by^ix  satellites  j  all  of 
which  were  discovered  by  Dr.  ETerschel^  and  revolve 
in  orbits  nearly  perpendicular  to  that  of  their  primary; 
C  Their  motion  is  apparently  retrograde  ;  but  this  is  pro- 
bably an  optical  illusion,  arising  from  the  difficulty  of 
ascertaining  which  part  of  their  orbits  inclines  towards 
the  earth,  and  which  declines  from  it.  They  are  reck- 
oned like  those  of  Jupiter.  • 

This  planet  is  not  uniformly  designated  by  the  name  Uranus.  Its 
discoverer  called  it  Georgium  Sidus,  and  it  is  often  called  Herschel. 
But  on  the  continent  of  Europe  it  has  obtained  the  name  Uranus. 
Different  writers  on  astronomy  use  diiferent  names. 


43.  It  was  stated  (No.  24,)  that  the  moon  turns  on  its 
axis  in  precisely  the  same  time  that  it  performs  its  revo- 
lution round  the  earth.  This  is  known  from  its  always 
presenting  to  us  the  same  side.  For  example,  at  its  full 
it  always  exhibits  the  same  spots  in  very  xiydny  uie 
same  place.  So  also  at  the  first  or  third  quarter  ;  that 
is,  in  quadrature,  /it  has  been  observed,  that  when  the 
seventh  satellite  oY  Saturn  is  to  the  eastward  of  that 
planet,  its  light  becomes  continually  weaker  till  it  • 
:1* 


22  Of  the  Planets. 

scarce  perceptible  ;  which  circumstance  must  arise 
from  dark  spots  or  regions  of  a  nature  to  reflect  little  or 
no  light,  which  extend  in  a  great  degree  over  the  side 
then  presented  to  us.  Now,  that^  this  phenomenon 
should  (thcmjs  occur,  when  this  satellite  is  precisely  in 
this  position,  it  is  necessary  that  it  revolve  round  its 
own  axis  in  the  same  time  that  it  revolves  round  Saturn: 
In  like  manner,  by  observing  periodical  changes  in  the 
intensity  of  the  light  of  Jupiter's  satellites,  Dr.  Herschel 
infers,  that  they  turn  on  their  axes  in  the  same  time  that 
they  occupy  in  moving  round  Jupiter.  |  Hence  it  ap- 
pears to  be  a  general  law  of  satellites,  that*  they  turn  on 
their  axes  in  the  same  time  in  which  they  revolve  round  their 
primaries. 

44.  On  this  account,  the  inhabitants  of  secondary 
planets  observe  some  singular  appearances,  which  the 
inhabitants  of  primary  planets  do  not.  fThose  who 
dwell  on  the  side  of  a  secondary  planet  next  to  the  pri- 
mary will  always  see  that  primary  ;  v.hile  those  who  live 
on  the  opposite  side  will  never  see  it.  Those,  who 
always  see  the  primary,  will  see  it  constantly  in  very 
neajfly  the  same  place.  For  example,  those  v/ho  dwell 
near  the  edge  of  the  moon's  disk,  Vvill  always  see  the 
earth  near  the  horizon,  and  those  in  or  near  the  centre 
will  always  see  it  directly  or  nearly  over  head.  Those 
who  dwell  in  the  moon's  south  limb  will  see  the  earth 
to  the  northward ;  those  in  the  north  limb  will  see  it  to 
the  southward  ;  those  in  the  east  limb  will  see  it  to  the 
westw^ard ;  w  hile  those  in  the  west  limb  \\'\\\  see  it  to 
eastward  ;  and  all  will  see  it  nearer  the  horizon  in  pro- 
portion to  their  own  distance  from  the  centre  of  the 
moon's  disk.  Similar  appearances  are  exhibited  to  the 
inhabitants  of  all  secondary  planets. 

It  may  be  necessary  for  young  pupils,  that  the  instructer  should 
illustrate  the  reason  of  these  appearances. 


Of  Comets.  23 

Sect.  11.      Of  Comets. 

45.  Besides  the  planets  above  described,  there  is 
another  class  of  bodies  revolving  about  the  sun,  which 
are  called  comets.  They  generally  move  in  orbits  very 
elliptical ;  at  one  time  coming  very  near  the  sun,  in  some 
instances  even  nearer  than  Mercury,  and  again  receding 
to  a  distance  far  beyond  the  orbit  of  Uranus.  The}' 
were  often  noticed  by  the  ancients ;  and  were  looked  upon 
as  harbingers  of  dire  calamity,  and  as  m.essengers  of 
vengeance  from  heaven.  But  modern  astronomers  look 
upon  them  as  bodies  solid  and  opa,que,  like  the  planets  ; 
revolving  round  the  sun,  like  them,  and  governed  by 
the  same  laws  ;  and  therefore  constituting  a  part  of  the 
solar  system.)  They  are  generally  distinguished  from 
all  other  heavenly  bodies,  fby  a  lucid  train  or  tail.  This 
tail  always  extends  in  a  direction  nearly  opposite  to  the 
sun.  It  is  of  various  lengths,  sometimes  scarcely  to  l>e 
seen,  and  sometimes  extending  through  90*^  or  even 
100^. ;  So  that  when  the  comet  sets  in  the  west,  its  tail 
extends  to  the  zenith^  that  is,  the  point  directly  over 
head. 

46.  CThe  magnitude  of  comets  has  been  observed  to 
be  very  different.^  Many  of  them  without  the  tail  ap- 
pear no  larger  than  stars  ;  while  others  have  been  seen 
immensely  larger.  One  is  said  to  have  been  visible  at 
Rome  in  the  reign  of  the  emperor  Nero,  which  was  not 
inferior  in  apparent  magnitude  to  tha  sun. :  The  astro- 
nomer Hevelius  also  observed  a  comet  in  1652,  which 
did  not  appear  to  be  less  than  the  moon,  though  it  was 
deficient  in  splendour  ;  having  a  pale,  dim  light,  and  ex- 
hibiting a  dismal  aspect.  '  Most  comets  appear  to  have 
a  very  dense  atmosphere  surrounding  their  bodies,  which 
very  much  weaken  the  sun's  rays  that  fall  on  them.  But 
notwithstanding  this,  when  the  sky  is  clear,  the  solid 
body  of  a  comet  often  reflects  a  very  splendid  light. 


24  Of  Comets. 

47.  The  number  of  comets  belonging  to  the  solar 
system  is  unknown.  Above  500  have  appeared  since 
the  commencement  of  the  Christian  era  ;  and  accounts 
of  many  more  are  extant.  The  orbits  of  the  comets  be- 
ing very  elliptical,  their  velocity  in  one  part  is  much 
greater  than  in  another.  They  are  also  turned  out  of 
their  course,  retarded  and  accelerated  by  the  attraction 
of  the  planets.  These  circumstances,  together  with  the 
difficulty  of  obtaining  the  elements  of  their  orbits,  ren- 
der all  calculations  of  their  periodical  times  extremely 
uncertain. 

(  Dr.  Halley  and  Professor  Encke  are  the  only  astrono- 
mers who  ever  successfully  predicted  the  return  of  a 
comet ;  and  these  in-  single  instances  only^  Of  three 
sanguine  calculations  of  Br.  Halley,  one"  has  proved 
correct,  one  has  entirely  failed,  and  one  remains  to  be 
tested.  Professor  Encke,  of  Seeberg  in  Germany, 
made  observations  on  a  comet  visible  in  1819,  and  cal- 
culated its  periodical  time  to  be  about  1200  days  only. 
He  predicted  its  return  in  1822  ;  but  owing  to  its  posi- 
tion it  would  not  be  visible  in  Europe  or  in  the  United 
States.  According  to  his  prediction  it  appeared  in 
1822,  and  was  visible  at  the  Islands  in  the  South  Pa- 
cific ocean.  It  is  but  a  small  body,  passing  in  its  peri- 
helion within  the  orbit  of  Mercury,  and  in  its  aphelion, 
midway  between  the  orbits  of  the  newly  discovered 
planets  and  that  of  Jupiter.  It  is  not  improbable  that 
this  body  will  ere  long  be  classed  with  the  planets. 

The  orbits  of  98  comets,  up  to  the  year  1808,  have  been  calculated 
from  observations  of  the  times  at  which  they  most  nearly  approached 
the  sun ;  their  distance  from  the  sun  and  from  the  earth  at  those 
times  ;  the  direction  of  their  movements  ;  the  places  at  which  their 
orbits  cut  the  ecliptic,  and  their  inclination  to  it.  The  result  is,  that 
of  these  98,  24  passed  between  the  Sun  and  Mercury,  33  between 
Mercury  and  Venus,  21  between  Venus  and  the  Earth,  16  between 
the  Earth  and  Mars,  and  4  between  Mars  and  Jupiter  ;  that  50  of 
these  comets  moved  from  east  to  west :  and  that  their  orbits  inclined 
at  every  possible  angle  to  the  ecliptic. 


Of  the  Stars.  '25 

When  comets  are  nearest  to  the  sim,  they  often  move  with  incredi- 
ble velocity.  Newton  calculated  the  velocity  of  the  comet  of  1680, 
when  nearest  the  sun, to  be  880,000  miles  an  hour  ;  and  Mr.  Squire, 
from  data  obtained  since  the  days  of  Newton,  has  computed  its  mo- 
tion to  be  1,240,108  miles  an  hour. 

The  comet  of  1758,  the  return  of  which  was  predicted  by  Dr.  Hal- 
ley,  was  looked  upon  with  great  interest  by  astronomers,  because  its 
return  icas  predicted.  But  four  revolutions  before,  in  1456,  it  was 
looked  upon  with  the  utmost  horror.  Its  long  tail  spread  consterna- 
tion over  all  Europe,  already  terrified  by  the  rapid  success  of  the 
Turkish  arms.  Pope  Callixtus,  on  this  occasion,  ordered  a  prayer,  in 
which  both  the  comet  and  the  Turks  were  included  in  one  anathema. 

Sect.  12.      Of  the  Stars. 

48.  All  the  heavenly  bodies,  of  which  we  have  not 
treated,  are  called  stars ;  and  except  comparatively  a 
few,  which  in  a  course  of  years,  appear  to  change  their 
places  tJiey  appear  to  be  fixed,  retaining  the  same  situ- 
tion  in  relation  to  each  other.  Their  number  is  un- 
known ;  but  we  are  commonly  very  much  deceived  in 
the  number  visible  to  the  naked  eye.  It  is  seldom  that 
so  many  as  1000  are  visible  at  once  in  the  clearest  night ; 
but  by  looking  at  them  confusedly,. we  imagine  them  to 
be  much  more  numerous.  They  are  classed  into  six 
magnitudes  ;  the  largest  are  of  the  firsts  magnitude,  and 
the  smallest  that  can  be  seen  by  the  naked  eye,  are  of 
the  6th. 

49.  We  have  no  certain  means  of  ascertaining  the 
distance  of  any  body  from  the  sun,  which  exceeds  200 
thousand  times  that  of  the  earth.  But  none  of  the  stars 
come  within  that  limit ;  so  we  cannot  determine  their 
real  distance.  It  is  generally  supposed  that  a  part,  if 
not  all  the  difference  in  the  apparent  magnitude  of  the 
stars  is  owing  to  a  difference  in  their  distances ;  the 
smallest  being  farthest  off.  Though  the  stars  generally 
appear  fixed,  yet  they  all  may  have  motion.  For  their 
distance  being  so  immensely  great,  (in  no  instance  less 
than  200  thousand  times  that  of  the  earth,  probably  much 


26  Of  the  Stars. 

more  in  general,)  a  rapid  motion  might  not  perceptibly 
change  their  relative  situation  in  two  or  three  thousand 
years. 

50.  As  telescopes  are  improved,  other  stars  become 
perceptible,  which  before  were  invisible.  (Many  stars 
also,  which,  to  the  naked  eye,  appear  single,  w  hen  seen 
through  a  telescope  appear  double,  treble,  or  even  qua- 
druple. Some  stars  are  subject  to  periodical  variations 
in  apparent  magnitude,  at  one  time  being  of  the  secona 
or  third,  and  at  another  of  the  fifth  or  sixth.  Some  have 
been  noticed  alternately  to  appear  and  disappear ;  be- 
ing visible  for  several  months,  and  again  invisible.  Se- 
veral stars  mentioned  by  ancient  astronomers  are  not 
now  to  be  found  ;  and  some  are  now  observed,  which 
•are  not  mentioned  in  the  ancient  catalogues.  ^ 

51.  In  a  clear  autum.nal  evening,  a  remarkably  light 
broad  zone  is  visible  in  the  heavens,  passing  from  north- 
east to  south-west.  This  appearance  is  usually  called 
the  Milky'ivay^  or  Galaxy.  It  is  generally  supposed  that 
this  appearance  is  owing  to  an  immense  number  of 
stars,  which,  from  their  apparent  nearness,  cannot  be 
distinguished  from  each  other.  Dr.  Herschel,  in  the 
course  of  J  of  an  hour,  saw  the  astonishing  number  of 
116,000  stars  pass  through  the  field  of  view  of  his  tele- 
scope, while  it  W'as  directed  to  the  milky-way.  Many 
whitish  spots  or  tracts,  called  nebulce,  are  visible  in  dif- 
ferent parts  of  the  heavens,  which  are  supposed  to  be 
milky-ways  at  an  inconceivable  distance. 

52.  The  stars  are  probably  suns,  around  each  of 
which  revolve  primary  and  secondary  planets,  as  about 
our  sun.  It  is  certain  that  they  do  not  reflect  the  light 
of  the  sun,  as  do  the  planets  ;  for  their  distance  is  so 
great,  that  they  would  not  in  such  case  be  visible.  The 
sun,  at  the  distance  of  a  star,  w^ould  certainly  appear  to 
us  no  larger  than  a  star  does.  Stars  are  distinguishable 
from  the  plaiiets  by  their  twinkling. 


Of  the  Stars.  27 

53.  The  ancients,  in  reducing  astronomy  to  a  science, 
Ibrmed  the  stars  into  covstelJatlonsy  by  applying  names  to 
particular  clusters.  This  arrangement  was  effected 
very  early,  and  is  the  most  ancient  monument  of  human 
skill.  The  choicest  efforts  of  art,  and  the  most  won- 
derful productions  of  labour,  4he  pride  and  ruin  of  em- 
pires of  the  greatest  known  antiquity,  have  passed 
away,  while  the  constellations  remain,  telling  of  people 
still  anterior.  Orion,  in  nearly  the  middle  of  which  is 
the  yard  i,  and  the  Pleiades,  commonly  called  the 
7  stars,  are  mentioned  in  the  book  of  Job,  the  oldest 
book  of  which  copies  are  extant  with  us.  The  number 
of  constellations  among  the  ancients  was  about  50  ;  the 
moderns  have  added  about  as  many  more.  On  the  ce- 
lestial globe,  the  largest  star  in  each  constellation  is 
usually  designated  by  the  first  letter  of  the  Greek  alpha- 
bet, and  the  next  largest  by  the  second,  and  so  on. 
When  the  Greek  alphabet  is  exhausted,  the  English  al- 
phabet, and  then  numbers,  are  used. 

54.  In  the  zodiac  are  12  constellations ^  of  the  sEune 
names  with  the  signs  of  the  zodiac  or  ecliptic.  But 
these  constellations  and  signs  do  not  coincide  ;*.but 
each  constellation  is  now  just  about.  30^  or  a  sign,  east- 
w^ard  of  the  sign  of  the  same  name.  For  example,  the 
constellation  Aries  is  30^  eastward  of  the  sign  Aries, 
and  the  constellation  Taurus,  30^  eastward  of  the  sign 
Taurus,  and  so  on.  Thus  the  sign  Aries  lies  in  the  con- 
stellation Pisces,  the  sign  Taurus  in  the  constellation 
Aries,  the  sign  Gemini  in  the  constellation  Taurus,  and 
so  on.  Hence  the  importance  of  distinguishing  between 
the  signs  of  the  Zodiac,  and  the  constellations  of  the  Zo- 
diac. The  cause  of  their  difference  will  be  noticed 
hereafter. 

Our  observations  of  the  stars  and  nebuloe,  are  confined  principally 
to  those  of  the  northern  hemisphere.  Of  the  constellations  near  the 
south  pole,  we  know  but  little ;  while  every  region  and  point  in  the 


§8  Of  the  Stars. 

northern  liemisphere  is  as  familiar  to  the  astronomer,  as  the  geogra- 
phy of  his  native  village.  The  following  beautiful  and  interesting  ex- 
tract is  from  Humboldt's  Personal  J^arrative  : — 

"  From  the  time  we  entered  the  torrid  zone,  we  were  never  wea- 
ried with  admiring,  every  night,  the  beauty  of  the  southern  sky, 
which,  as  we  advanced  the  south,  opened  new  constellations  to  our 
view.  We  feel  an  indescribable  sensation,  when,  on  approaching 
the  equator,  and  particularly  on  passing  from  one  hemisphere  to  the 
other,  we  see  those  stars,  which  we  have  contemplated  from  our  in- 
fancy, progressively  sink  and  finally  disappear.  Nothing  awakens  in 
the  traveller  a  livelier  remembrance  of  the  immense  distance  by 
which  he  is  separated  from  his  country,  than  the  aspect  of  an  un- 
known firmament.  The  grouping  of  the  stars  of  the  first  magnitude, 
scattered  nebulae,  rivalling  in  splendour  the  milky  way,  and  tracks 
of  space  remarkable  for  their  extreme  blackness  give  a  particular 
physiognomy  to  the  southern  sky.  This  sight  fills  with  admiration 
even  those,  who,  uninstructed  in  the  branches  of  accurate  science, 
feel  the  same  emotion  of  delight  in  the  contemplation  of  the  heaven- 
ly vault,  as  in  the  view  of  a  beautiful  landscape,  or  a  majestic  site. 
A  traveller  has  no  need  of  being  a  botanist,  to  recognise  the  torrid 
zone  on  tne  mere  aspect  of  its  vegetation  ;  and  without  having  ac- 
quired any  notions  of  astronomy,  without  any  acquaintance  with  the 
celestial  charts  of  Flamstead  and  de  la  Caille,  he  feels  he  is  not  in 
Europe,  when  he  sees  the  immense  constellation  of  the  Ship,  or  the 
phosphorescent  clouds  of  Magellan,  arise  on  the  horizon.  The  heaven, 
and  the  earth,  every  thing  in  the  equinoctial  regions,  assumes  an  ex- 
otic character. 

.  "  The  lower  regions  of  the  air  were  loaded  with  vapours  for  some 
days.  We  saw  distinctly  for  the  first  time  the  Cross  of  the  south,  in 
the  sixteenth  degree  of  latitude  ;  it  was  strongly  inclined,  and  appear 
ed  from  time  to  time  between  the  clouds,  the  centre  of  whi  ",h,  furrow- 
ed by  uncondensed  lightnings,  reflected  a  silver  light.  If  a  traveller 
may  be  permitted  to  speak  of  his  personal  emotions,  I  shall  add,  that 
in  this  night  I  saw  one  of  the  reveries  of  my  earliest  youth  accom- 
plished. 

"  When  we  begin  to  fix  our  eyes  on  geographical  maps,  and  read 
the  narratives  of  navigators,  we  feel  for  certain  countries  and  cli- 
mates a  sort  of  predilection,  for  which  we  know  not  how  to  accou:\t 
at  a  more  advanced  period  of  life.  These  impressions,  however,  ex- 
ercise a  considerable  influence  over  our  determinations  ;  and  from  a 
sort  of  instinct  we  endeavour  to  connect  ourselves  with  objects,  on 
which  the  mind  has  long  been  fixed  as  by  a  secret  charm.  At  a  peri 
od  when  I  studied  the  heavens,  not  with  the  intention  of  devoting 
mvself  to  astronomy,  but  only  to  acquire  a  knowledge  of  the  stars,  1 
was  agitated  by  a  fear  unknown  to  those  who  love  a  sedentary  life. 
It  seemed  painful  to  me  to  renounce  the  hope  of  beholding  those 
beautiful  constellations,  which  border  the  southern  pole.  Impatient  to 
rove  in  the  equinoctial  regions,  I  could  not  raise  my  eyes  towards  the 
starry  vault  without  thinking  of  the  Cross  of  the  south. 


Of  the  Stars.  29 

"  The  pleasure  we  felt  on  discovering  the  southern  Cross  wa-a 
warmly  shared  by  such  of  the  crew  as  had  lived  in  the  colonies.  Ii; 
the  solitude  of  the  seas,  we  hail  a  star  as  a  friend,  from  whom  we  have 
long  been  separated.  Among  the  Portuguese  and  the  Spaniards  pe 
culiar  motives  seem  to  increase  this  feeling  ;  a  religious  sentiment 
attaches  them  to  a  constellation,  the  form  of  which  recalls  the  sign  of 
'-he  faith  planted  by  their  ancestors  in  the  deserts  of  the  new  world. 

''  The  two  great  stars  which  mark  the  summit  and  the  foot  of  the 
"^ross  having  nearly  the  same  right  ascension,  (see  No.  64,)  it  follows 
ence,  that  the  constellation  is  almost  perpendicular  at  the  moment 
when  it  passes  the  meridian.  This  circumstance  is  known  to  every 
nation,  that  lives  beyond  the  tropics,  or  in  the  southern  hemisphere. 
It  has  been  observed  at  what  hour  of  the  night,  in  different  seasons, 
the  Cross  of  the  south  is  erect,  or  inclined.  It  is  a  time-piece  that 
advances  very  regularly  near  four  minutes  a  day,  and  no  other  group 
of  stars  exhibits  to  the  naked  eye  an  observation  of  time  so  easily 
made.  How  often  have  we  heard  our  guides  exclaim  in  the  savannas 
of  Venezuela,  or  in  the  desert  extending  from  Lima  to  Truxillo, 
*  Midnight  is  past,  the  Cross  begins  to  bend  I'  How  often  those  words 
reminded  us  of  that  affecting  scene,  where  Paul  and  Virginia,  seated 
near  the  sources  of  the  river  of  Lataniers,  conversed  together  for  the 
last  time,  and  where  the  old  man,  at  the  sight  of  the  southern  Cross, 
warns  them  that  it  is  time  to  separate." 

4 


Mamj  of  the  fads  stated  above,  with  some  others  relating  to  the 
oodies  ichich  compose  the  solar  system,  are  arranged  in  the  following 
tables,  useful  for  reference,  hut  not  necessary  to  be  learned. 

TABLE  I. 


Of 

the  Sun  and  Primary  Planets. 

a 

^ 

^ 
^ 

o 

^ 

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pT 

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T'.ose  figures  marked  t  are  tm?^  certain. 


TABLE  II. 


31 


Of  Secondary  Planets. 


o 

1 

03 

o 

d    h     1 
1  18  27 
3  13  14 
7    3  42 
16  16  32 

CO 
CO 

O 

m 
O 

'5 

1^ 

d    h     / 
5  21  25 

816  57 

10  23    4 

13  10  56 

38    148 

10716  40 

=  o 

CO         i> 

i    UO) 

CO  mO  6  6  6  6  6 

o  §    8 

o    /     // 
3  18  38 
3  18     0 
3  13  58 
2  36    0 

h 

224.155 

290.821 
339.052 
388.718 
777.481 
1.555.872 

o 
11 

Q 

Miles. 
264.490 
420.815 
671.2:^4 
1.180.582 

^      t=S>>> 

^^G> 

d 

m 

"^ 
o 

'o 

Id 

® 

o 

•T3 

ii 
1^ 

d  h   / 

0  22  37 

1  8  53 

1  21  18 

2  17  44 
4  12  25 

15  22  41 
79     7  54 

i 

© 
O 

1%A 

d    h     ' 

27  7  43 
Bulk  (that  of 

change,  29d. 

J:? 

"  1:i  ti 

h5  -^ -^ 

S5 

to 

'=2.5' 

o     / 
5    50 

eter  2159.- 
1)  1—49. 
change  to 

2  s 

119.627 
153.496 
190.044 
243.449 
240.005 
788.258 
2.297.541 

r 

Miles. 
240,000 

Moon's  diam 
the  earth  being 

Period  from 
12h.  44'. 

•—1 

3*  Of  Latitvde  and  Longitude. 

CHAP.  11. 
LATITUDE  AND  LONGITUDE. 

^b.  When  latitude  and  longitude  are  applied  to  places 
on  the  earth,  they  properly  belong  to  geography.  But 
as  the  method  of  finding  them  is  purely  astronomical,  it 
is  proper  to  treat  of  them  as  used  both  to  designate 
the  situation  of  places  on  the  earth,  and  of  the  hea- 
venly bodies.  Before  any  thing  can  be  understood  of 
latitude  and  longitude,  definite  ideas  must  be  obtained 
of  the  poles^  the  equator^  parallels  of  latitude,  and  me- 
ridians. The  earth  turns  round  on  an  imaginary  line, 
passing  through  its  centre,^  called  its  axis ;  the  extre- 
mities of  this  axis  are,  as  before  stated,  called  poles; 
one  north  pole,  the  other  south.  If  the  axis  be  suppos- 
ed to  extend  both  ways  to  the  starry  heavens,  its  places 
or  points  among  the  stars  are  the  celestial  poles,  one 
north,  and  the  other  south,  directly  over  or  beyond  the 
poles  of  the  earth  of  the  same  name.  The  north  celes- 
tial pole  is  very  near  a  particular  star,  which  on  that  ac- 
count is  called  the  pole  star, 

56.  The  equator  is  a  circle  surrounding  the  earth 
from  west  to  east,  at  equal  distance  from  the  poles. 
Hence  the  equator  divides  the  earth's  surface  into  two 
equal  parts,  called  hemispheres.  If  the  plane  of  the 
equator  were  extended  e^^ery  way  to  the  starry  heavens, 
the  circle  it  would  make  among  the  stars  is  called  the 
celestial  equator.  It  is  l  ^m  the  equator  that  latitude 
on  the  earth  is  reckoned.  All  places  between  the 
equator  and  the  north  pole  are  in  north  latitude,  and  all 
places  between  the  equator  and  the  south  pole  are  in 
south  latitude.  The  latitude  is  greater,  as  the  place  is 
fa»-ther  from  the  equator  and  nearer  the  poles.  All  cir- 
cles passing  round  the  eaith  from  west  to  east  between 


Of  Latitude  and  Longitude,  33 

the  equator  and  the  poles,  are  called  parallels  of  laii 
tude ;  and  when  two  places,  as  Boston  and  Philadel- 
phia, differ  in  latitude,  they  are  said  to  be  on  different 
parallels.    (There  may  be  as  many  parallels  as  there  are 
places  not  equally  distant  from  the  equator. 

57.  /A  line  passing  over  the  earth  from  the  north  to 
the  south  pole,  and  crossing  the  equator  at  right  angles,^' 
is  called  a  meridian.  Every  place  on  the  earth's  sur- 
face may  be  supposed  to  have  such  a  line  or  circle  pass- 
ing through  it ;  consequently,  when  a  place  lies  more 
easterly  or  westerly  than  another,  it  is  said  to  have  a 
different  meridian.  Hence  there  may  be  as  many 
meridians,  as  there  are  places  lying  eastwardly  and 
westwardly  of  each  other.  When  places  are  on  differ-, 
ent  meridians,  they  are  said  to  be  in  different  longitude.; 

/^Celestial  meridians  are  lines  passing  among  the  stars" 
from  one  celestial  pole  to  the  other,  crossing  the  celes- 
tial equator  at  right  angles.  When  it  is  noon  at  any 
place,  the  sun  is  in  the  celestial  meridian  directly  over 
the  meridian  of  that  place. 

Let  the  instructer  explain  right  angles. 

58.  (To  illustrate  what  has  been  said,  let  PI.  III.  fig. 
1.  represent  the  earth.  The  line  N'S  is  its  axis;  the 
extremities  of  which,  JV  and  S,  are  the  north  and  south 
poles  of  the  earth.  jBQ  shows  the  equator.  The  lines 
10  10,  20  20,  30  30,  &c.  are  parallels  of  latitude  ;  and 
tlie  lines  JVAS,  JVBS,  &c,  are  meridians.  If  each  of 
these  meridians  be  supposed  to  extend  quite  round  the 
earth,  (as  they  do  on  the  artificial  globe,)  each  would 
divide  it  into  an  eastern  and  western  hemisphere  ;  just 
as  the  equator  divides  it  into  northern  and  southern. 

Much  of  what  is  said  in  this  chapter  may  be  illustrated  with  a 
terrestrial  and  celestial  globe,  if  at  hand,  far  better  than  by  any 
figure. 

59.  Latitude  and  longitude  are  expressed  in  degrees 


34  Qf  Latitude  and  Longitude, 

and  minutes.  fThe  latitude  of  a  place  on  the  globe  is 
estimated  by  the  number  of  degrees  on  its  meridian  be- 
tween the  equator  and  that  place,  For  example,  the 
place  X  is  in  latitude  40°  north,  because  40^  of  its  me- 
ridian lie  between  the  equator  and  it.  ^T^he  longitude 
of  one  place  from  another  is  determined  by  the  number 
of  degrees  there  are  on  the  equator,  between  the  me- 
ridian of  one  and  the  meridian  of  the  other.  For  ex- 
ample, the  place  v  is  20^  west  longitude  froni  x,  and 
X  is  20^  east  longitude  from  v,  because  20^  of  the  equa- 
tor lie  between  the  meridians  of  v  and  x ;  as  may  be 
seen  by  the  figures  under  the  equator. 

60.  Of  all  the  lines  or  circles  passing  round  the  earth 
from  west  to  east,  it  is  obvious  that  the  equator  is  the 
only  one  which  constitutes  a  great  czVc/e,;that  is,  divides 
the  eartKs  surface  into  two  hemispheres^  "All  the  rest 
are  less  circles^  that  is,  divide  the  eajWs  surface  into 
two  unequal  parts;  and  more  unequal  as  the  circles 
are  T-rther  from  the  equator  and  nearer  the  poles.  On 
this  account  it  is  much  more  natural  to  reckon  latitude 
from  the  equator  than  from  any  other  line  or  circle. 
But  all  the  meridians  are  great  circles,  each  dividing 
the  earth's  surface  into  two  hemispheres.  (Hence  there 
is  no  natural  reason  why  longitude  should  be  reckoned 
from  one  meridian  rather  than  from  another!  Hence 
it  w^as  customary,  till  very  lately/for  w  riters  of  different 
nations  to  estimate  longitude  from  different  meridians, 
each  selecting  that  of  the  capital  of  his  own  country  as 
the  first  or  prime  meridian^  and  reckoning  the  longitude 
of  all  other  places  from  this.  Thus  French  writers  es- 
timated longitude  from  the  meridian  of  Paris ;  British 
from  that  of  London ;  American  from  that  of  Philadel- 
phia, and  afterwards  of  Washington.  The  obvious 
confusion  and  inconvenience  of  this  practice  at  length 
induced  writers  in  Europe  and  America  to  fix  upon  one 
prime  meridian ;  and  for  this  purpose  selected  that  of 


Of  Latitude  and  Longitude.  35 

the  Royal  Observatory  at  Greenwich,  near  London. 
Hence,  on  most  maps  and  charts  recently  published, 
longitude  is  laid  down  from  the  meridian  of  London  or 
Greenwich. 

6\,  The  equator  being  once  assumed  as  the  circle 
from  which  to  reckon  latitude,  the  poles  become  natu- 
ral limits  beyond  which  it  cannot  be  reckoned.  For 
if  latitiule  be  reckoned  beyond  the  poles  on  one  side, 
the  equator  is  approached  on  the  other.  Hence  no 
place  can  have  latitude  exceeding  90^,  the  distance 
from  the  equator  to  the  poles.  Having  agreed  upon  a 
certain  meridian  from  which  to  reckon  longitude  both 
east  and  west,  the  opposite  part  of  that  meridian,  con- 
tinued roimd  the  earth,  becomes  the  limit  of  longitude, 
which  is  obviously  half  a  circle  or  180^  from  the  prime 
meridian.  Hence  no  place  on  the  earth's  surface  can 
have  more  than  180^  longitude,  and  if  a  place  has  180^ 
longitude,  it  may  be  either  east  or  west. 

62.  But  the  latitude  and  longitude  of  heavenly  bodies 
are  estimated  somewhat  differently  from  those  of  places 
on  the  earth's  surface.  It  has  been  stated  that  the  cir- 
cle among  the  stars  which  the  plane  of  the  equator,  ex- 
tended every  way  to  the  starry  heavens,  would  de- 
scribe, is  called  the  celestial  equator.  Now  this  celes- 
tial equator  does  not  coincide  with  the  ecliptic,  but 
makes  an  angle  with  it  of  23J^,  that  is,  the  earth's  axis 
is  not  perpendicular  to  the  plane  of  the  ecliptic,  but  is 
inclined  23 Jo.  (See  PI.  V.  fig.  1.)  Thus  we  have  two 
great  circles,  the  ecliptic  and  equator,  passing  through 
the  heavens  eastwardly  and  weStwardly,  from  which 
the  latitude  of  the  heavenly  bodies  might  be  estimated. 
Astronomers  have  selected  the  ecliptic  for  this  purpose, 
and  have  supposed  lines  or  circles  to  cross  it  at  right 
angles,  as  the  meridians  do  the  equator ;  w  hich  lines  or 
circles  are  called  secondaries  to  the  ecliptic.  The 
points  where  all  the  secondaries  to  the  ecliptic  meet. 


36  Of  Latitude  and  Longitude. 

are  called  the  poles  of  the  ecliptic ;  <^Vhich  points  are 
23^^  from  the  celestial  poles. 

This  No.  should  be  illustrated  and  explained  to  young  pupils ; 
familiar  examples  will  readily  occur  to  the  instructer. 

63.  Hence  the  latitude  of  a  heavenly  body  is  its  dis- 
tance from  the  ecliptic,  on  a  secondary  to  the  ecliptic 
passing  through  it ;  and,  like  latitude  on  the  earth,  can 
never  exceed  90^.  The  longitude  of  a  heavenly  body 
is  the  distance  of  a  secondary  to  the  ecliptic  passing 
through  it,  from  some  uniform  prime  secondary.  But 
the  longitude  of  heavenly  bodies,  unlike  longitude  on  the 
earth,  is  reckoned  only  eastward ;  consequently  it  may 
extend  to  360^.  It  is  usually  stated  in  signs,  degrees, 
minutes,  &c.  ;  and  the  prime  secondary,  from  which  it 
is  reckoned,  cuts  the  ecliptic  in  the  beginning  of  the 
sign  Aries,  a  point  where  the  celestial  equator  crosses 
the  ecliptic.  Thus,  if  a  secondary,  passing  through  a 
heavenly  body,  cuts  the  ecliptic,  say  18°  in  the  sign 
Capricorn,  the  longitude  of  that  body  is  9  signs,  18°. 

If  a  celestial  globe  be  at  hand,  the  pupil  may  be  exercised  in 
finding  the  latitude  and  longitude  of  some  of  the  principal  stars,  &c. 
See  Appendix,  Sect.  VIII.  Proh.  XIX. 

64.  But  it  is  often  important  to  know  the  distance  of 
a  heavenly  body  from  the  celestial  equator,  as  well  as 
from  the  ecliptic.  This  distance  is  its  declination^  and 
is  reckoned  on  a  meridian  as  latitude  is  on  the  earth. 
Its  distance  from  the  beginning  of  Aries,  reckoned  on 
the  equator,  is  its  right  ascension;  which,  like  celestial 
longitude,  is  reckoned  through  the  whole  circle,  or  360°. 

The  learner  should  have  a  distinct  idea  of  the  difference  between 
celestial  latitude  and  declination,  that  one  is  reckoned  from  the 
ecliptic  and  the  other  from  the  equator.  Also  of  longitude  and  right 
ascension,  that  one  is  reckoned  on  the  ecliptic  and  the  other  on  the 
equator  ;  and  both  from  the  same  point,  viz.  the  beginning  of  Aries, 

65.  Let  us  return  to  the  consideration  of  terrestrial 


Of  Latitude  and  Longitude'  37 

latitude  and  longitude.  As  the  latitude  of  a  place  is  its 
distance  from  the  equator  measured  on  its  meridian, 
and  all  meridians  are  great  circles  and  consequently 
equally  large,  it  is  obvious  that  a  degree,  or  g^^  part, 
of  one  is  equal  to  the  same  part  of  another.  Hence 
degrees  of  latitude  are  all  of  the  same  absolute  length, 
containing  60  geographical,  or  69^  statute  miles  of  320 
rods.  Thus,  if  two  places  on  the  same  meridian, 
whether  near  the  equator  or  distant  from  it,  differ  in 
latitude  2°,  their  absolute  distance  from  each  other  is 
60  X  2  =:  120  geographical  miles,  or  69J  X  2  zz:  139 
statute  miles. 

The  statements  in  this  No.  are  not  strictly  true,  because  the  earth 
is  not  a  perfect  globe,  as  will  be  shown  hereafter.  But  the  earth  is 
BO  nearly  a  perfect  sphere,  that  it  is  always  so  represented  on  maps 
and  globes. 

66.  Witli  regard  to  longitude,  the  case  is  different. 
The  equator  is  a  great  circle  like  a  meridian ;  and  a 
degree,  or  ^\-^  part  of  it,  is  equal  to  the  same  part  of  a 
meridian ;  and  consequently  a  degree  of  longitude  on 
the  equator  is  equal  to  a  degree  of  latitude.  But  the 
parallels  of  latitude  are  not  great  circles,  but  are  con- 
tinually becoming  less  as  they  are  farther  from  the 
equator  and  nearer  the  poles.  Consequently  a  degree, 
or  3^^^  part,  of  one  parallel  is  not  equal  to  the  same 
part  of  another  parallel,  nor  to  the  same  part  of  the 
equator.  For  example,  the  places  x  and  v  are  20^ 
apart  (PI.  III.  fig.  1.)  ;  but  obviously  they  are  not  so 
many  miles  apart  as  they  would  be,  if  situated  on  the 
same  meridians  at  the  equator ;  and  further  apart,  than 
if  situated  on  the  same  meridians  nearer  the  poles. 
Hence  it  is  obvious,  that  as  latitude  increases^  the  length 
of  a  degree  of  longitude  decreases  ;  and  when  the  latitude 
is  90^,  longitude  vanishes. 

At  the  close  of  this  Chapter  is  a  Table,  showing  the  length  of  a, 
degree  of  longitude  for  every  degree  of  laiitude. 


38  Of  Latitude  and  Longitude, 

67.  What  has  been  said  will  enable  us  readily  to 
find  a  place  on  a  globe,  map,  or  chart,  when  its  latitude 
and  longitude  are  stated.  But  the  question  forces  it- 
self upon  us,  how  were  the  latitude  and  longitude  first 
ascertained  ?  I  look  on  the  map  of  the  world,  and  find 
Boston  placed  in  latitude  about  42J°  north,  and  in  lon- 
gitude little  more  than  70^  west.  But  how  did  he,  who 
first  gave  Boston  this  place,  know  that  such  was  its  real 
latitude  and  longitude  ?  He  could  not  go  to  the  equa- 
tor and  measure  its  latitude ;  he  could  not  go  to  Lon- 
don and  measure  its  longitude.  Or  how  can  the  lati- 
tude and  longitude  of  a  vessel  be  found,  when  driven 
about  in  the  ocean  and  constantly  changing  its  situation? 
The  compass  will  show  the  mariner  in  what  direction 
his  vessel  is  going,  but  it  will  not  show  him  the  port  he 
has  left,  nor  that  which  he  wishes  to  reach. 

68.  The  horizon  is  the  circle  where  the  visible  sky 
and  land  or  water  meet.  For  example,  when  the  sun 
rises,  he  comes  above  the  horizon ;  when  he  sets,  he 
sinks  below  the  horizon.  When  the  plane  of  the  hori- 
zon is  supposed  to  just  touch  the  earth's  surface,  the 
horizon  is  called  sensible ;  but  when  the  plane  is  sup- 
posed to  pass  through  the  earth's  centre,  the  horizon  is 
called  rational.  Thus,  (PL  I.  fig.  3.)  if  E  be  the  earth, 
the  line  ah  represents  the  plane  of  the  sensible  horizon, 
and  ed  that  of  the  rational.  But  the  distance  of  the 
heavenly  bodies  is  so  great,  that  the  diflTerence  betiveen 
the  sensible  and  rational  horizon  is  not  perceptible; 
and  when  they  rise  above  or  sink  below  the  rational, 
they  at  the  same  time  appear  to  rise  above  or  sink  be- 
low the  sensible.  We  shall  therefore  for  the  present 
consider  them  as  one  ;  but  uniformly,  when  the  word 
horizon  occurs  in  this  treatise,  the  rational  is  meant,  if 
the  sensible  be  not  stated.  When  a  distinct  idea  of  the 
horizofx  18  obtained,  it  will  be  obvious,  that  the  zenith^ 
or  point  directly  over  head  is  always  exactly  9(P  from 


Of  Latitude  and  Longitude.  30 

every  part  of  tlie  horizon.     The  iiadir  is  the  point  in  the 
heavens  exactly  opposite  to  the  zenith. 

The  Zenith  and  JVadir  are  sometimes  called  the  poles  of  the  hori- 
zon ;  they  being  to  the  horizon,  what  the  celestial  poles  are  to  the 
equator. 

69.  The  zenith  of  any  place  is  just  as  many  degrees 
from  the  celestial  equator,  as  that  place  is  from  the 
eartKs  equator.  Let  SEJV^  be  the  earth,  (PI.  II. 
fig.  4.)  SJV  its  axis,  and  £Q  the  equator.  Let  eg  ^ 
be  90°  of  a  circle  in  the  starry  heavens,  equal  to  E  o  JV, 
90°  of  a  meridian  on  earth.  To  a  person  at  E  on  the 
earth's  equator,  the  point  e,  in  the  celestial  equator, 
will  be  in  the  zenith.  If  the  person  move  from  E 
through  0  to  A^  (90°),  every  successive  point  in  e  ^  '^ 
(90°),  will  come  into  the  zenith  ;  so  that  when  he  comes 
to  JV,  "^  will  be  in  the  zenith.  And  in  like  manner,  if 
he  move  through  any  part,  as  jEo,  (40°),  the  zenith  will 
be  at  g,  40°  from  the  celestial  equator.  Hence  it  is 
obvious,  that  if  the  distance  of  the  zenith  of  any  place 
from  the  celestial  equator  can  be  found,  it  will  show  the 
latitude  of  that  place. 

70.  It  is  to  be  noticed,  that  as  a  person  changes  his 
latitude,  the  plane  of  the  horizon  changes  its  position. 
For  example,  to  a  person  at  jE,  on  the  equator,  the 
line  DSJY^  will  represent  the  plane  of  the  horizon ; 
and  both  the  terrestrial  and  celestial  poles  will  be  in  the 
horizon.  But  if  he  move  from  the  equator  towards 
either  pole,  say  JV,  and  come  to  o,  then  the  plane  of 
the  horizon  is  represented  by  the  line  HO.  Here  the 
pole  star  ^  will  not  be  in  the  horizon,  but  above  it ;  and 
just  as  far  above  it  as  the  zenith  g  is  from  the  celestial 
equator  e.  For  the  horizon  is  always  just  90°  every 
way  from  the  zenith.  Hence  it  is  just  as  far  from  g  to 
J,  as  from  e  to  ^  5  consequently  just  as  far  from  ^  to  cf, 
as  from  g  to  e.  Therefore,  in  order  to  find  the  dis- 
tance of  the  zenith  of  any  place  from  the  celestial  equa- 


40  Of  Latitude  and  Longitude 

tor,  (which  is  just  the  same  as  the  latitude  of  that  place,; 
tt  is  only  necessary  to  measure  the  height  of  the  celestial 
pole  above  the  horizon.  This  can  be  readily  done  by  an 
instrument  called  a  quadrant. 

In  order  to  show  how  the  altitude^  or  height  of  a  heavenly  body 
above  the  horizon,  can  be  ascertained,  lei  A  a  e  (PI.  III.  fig.  2.)  be 
a  quadrant,  that  is  a  quarter  of  a  circle  :  its  circular  edge  being  di- 
vided into  90°,  and  each  degree,  when  practicable,  divided  into 
minutes,  &c.  Let  o,  o,  be  small  sight  holes,  and  ^  r,  a  plumb-line, 
nanging  loose  from  the  point  A.  Let  *1  be  in  the  horizon,  and 
■*2  in  the  zenith.  It  is  obvious,  that,  when  the  quadrant  is  so  held 
that  the  *]!.  in  the  horizon  is  seen  through  the  sights  o,  o,  the 
plumb-line  will  hang  by  the  edge  A  e.  But  if  the  quadrant  be 
turned  gradually  towards  B,  the  plumb-line  will  successively  in- 
ersect  the  divisions  of  the  quadrant,  10,  20,  30,  &c. ;  and  when 
the  zenith  *2  is  seen  through  the  sights  o,  o,  the  plumb-line  will 
coincide  with  the  edge  A  a.  Thus,  while  the  eye  directed  through 
o,  o,  successively  passes  over  90°  of  the  heavens,  the  plumb-line 
passes  over  90°  of  the  quadrant.  And  just  so  of  any  part.  For 
sxample,  if  the  *3,  40°  above  the  horizon,  be  seen  through  o,  o,  the 
plumb-line  intersects  the  40th  degree,  on  the  divided  or  graduated 
edge  of  the  quadrant. 

The  place  of  the  north  celestial  pole  is  very  nearly  marked  by 
the  pole  star  ;  and  the  situation  of  the  south  is  so  well  described, 
that  little  difficulty  is  experienced  in  ascertaining  it. 

71.  But  this  method  of  ascertaining  latitude  can  be 
practised  only  by  night,  when  the  stars  are  visible. 
Tills  is  sufficient  on  land ;  but  at  sea  it  is  often  neces- 
sary to  find  the  latitude  by  day.  This  can  be  readily 
donr  by  taking  the  height  of  the  sun  at  noon,  called  its 
meriaian  altituae.  For  if  the  sun  be  in  the  celestia 
equator  e,  and  a  person  at  i  notices  with  a  quadrant  its 
distance  from  H,  the  horizon,  by  subtracting  this  dis- 
tance from^  e  iJ,  (90^),  the  distance  g  e,  or  the  lati- 
tude of  0,  is  ascertained.  But  if  the  sun  be  not  in  the 
celestial  equator,  but  have  either  north  or  south  declina- 
tion(  this  declination  must  be  first  found  by  a  nautical 
almanac  or  a  common  globe,  and  added  to  or  subtract- 
ed from  the  sun's  meridian  altitude.  For  it  is  the 
leight  of  the  equator  and  not  of  the  sun,  which  must  be 


V 


Of  Latitude  and  hongitude,  4 1 

taken  from  90^.  For  example,  if  the  sun  be  at  r,  with 
a  north  decHnation  of  5^^,  this  5^  must  be  taken  from 
the  meridian  altitude  of  the  sun,  and  it  gives  the  height 
of  the  celestial  equator ;  which  being  taken  from  DO^, 
gives  the  latitude  of  o.  But  if  the  sun's  declination 
were  south  in  the  above  case,  it  must  be  added  to  the 
sun's  meridian  altitude.  These  methods  of  finding 
latitude  are  generally  sufficient;  but  there  are  others 
which  may  be  practised  if  necessary. 

It  may  be  useful  to  subjoin  the  following  rule.  When  the  lati- 
tude and  declination  are  both  north  or  both  soath,  the  declination 
must  be  subtracted  from  the  sun's  meridian  altitude  ;  but  i^  <yne  hp, 
north  and  the  other  south,  it  must  be  added. 

72.  A  very  common  way  of  ascertaining  longitude 
at  sea  will  here  be  noticed,  but  not  explained.  It  is  by 
what  is  called  the  ship's  reckoning;.  That  is,  the  direc- 
tion, in  which  the  vessel  sails  is  noted,  and  the  distance 
that  she  sails  is  estim'^^'^d  by  an  instrument,  called  the 
log.  Having  the  direction  or  the  course^  as  it  is  called, 
and  the  distance,  the  latitude  and  longitude  may  be 
ascertained  by  a  common  traverse  table.  But  this 
method  is  very  inaccurate  and  not  to  be  depended 
upon,^^n  account  of  currents  in  the  ocean,  tempests 
and  unequal  force  of  winds.  Hence  navigators  have 
recourse  to  heavenly  bodies  for  this  purpose. 

73.  When  the  sun,  in  his.  apparent  daily  course 
round  the  earth,  comes  to  the  meridian  of  any  place,  it 
is  noon  at  all  places  on  that  meridian,  after  noon  at  all 
places  eastward  of  that  meridian,  and  before  noon  at 
all  places  westward  of  it.  For  as  the  apparent  course 
of  the  sun  is  from  east  to  west,  it  is  obvious  that  he  will 
come  to  the  meridian  of  any  place  sooner,  as  that  place 
lies  more  easterly ;  and  later  as  it  lies  more  westerly. 
In  24  hours,  the  sun  appears  to  complete  a  revolution, 
i,  e,  to  pass  through  the  whole  circle  of  the  heavens 
or   360^.      Consequently  he   appears  to  pass  through 

5 


42  Of  Latitude  and  Longitvde. 

(360 -^24)  ={159'  every  hour.  Hence,  when  it  is 
noon  at  a  particular  place,  as  Boston,  it  will  be  1  o'clock 
at  all  places  on  a  meridian  15^  east  of  that  of  Boston, 
and  11  o'clock  at  all  places  on  a  meridian  15^  west  of 
that  of  Boston. ,  If  the  distance  of  two  meridians  be 
30^,  the  difference  of  time  is  2  hours,  and  so  on. 

74.  Hence  it  is  plain  that  as  places  differ  in  longi- 
tude, that  is,  are  situated  on  different  meridians,  the 
clocks  and  watches  of  those  places  will  show  different 
hours  at  the  same  instant  of  absolute  time  ;  a  difference 
of  15^  always  producing  a  difference  of  1  hour  in  time. 
For  example,  Paris  is  2J^  east  longitude  from  London. 
This  difference  at  the  rate  of  1  hour  for  15^,  produc<iS 
a  difference  of  time  of  9  minutes  22  seconds.  Hence 
the  clocks  at  Paris  are  9  minutes  22  seconds  faster 
than  those  of  London ;  so  that  when  it  is  noon  at  Lon- 
don it  is  9  minutes  22  seconds  past  noon  at  Paris.  So 
also  the  difference  of  longitude  between  London  and 
Boston  is  71°  4^;  consequently  the  difference  of  time 
by  the  clocks  at  Boston  and  London  is  4  hours  44  mi- 
nutes 16  seconds.  Hence  when  it  is  noon  at  Boston,  it 
wants  15  minutes  44  seconds  of  5  o'clock  at  London ; 
and  when  it  is  noon  at  London  it  is  15  minutes  44 
seconds  after  7  in  the  morning  at  Boston. 

75.  Hence,  if  the  difference  of  time,  as  shown  by 
the  clocks  of  two  places,  is  known,  the  difference  of 
longitude  between  them  can  be  ascertained.  Suppose 
I  have  a  watch  of  such  workmanship,  and  so  well  regu- 
lated, that  it  would  always  show  the  exact  time  at  Lon- 
don ;  by  this  I  can  find  my  longitude.  For  by  observ- 
ing the  precise  time  when  the  sun  comes  to  the  meri- 
dian where  I  am,  I  know  it  is  12  o'clock  where  I  am; 
and  by  looking  at  my  watch,  I  know  what  the  time  is 
at  London.  Then,  by  allowing  1  hour  for  15°,  I  know 
my  longitude. 

76.  To  illustrate  this,  suppose  I  am  sailing  m  the 


Of  Latitude  and  Longitude.  43 

Mediterranean  sea,  and  v»isli  to  know  my  longitude. 
When  the  sun  is  exactly  south,  and  T  know  it  to  be 
noon  where  I  am,  I  iind  by  my  watch  that  it  wants  20 
minutes  of  11  o'clock  at  London.     The  difference  in 
time   is   1    hour  20  minutes.      I  am,   therefore,  on  a 
meridian   20°   from  that  of   London  ;    and   eastward, 
because  it  is  noon  where  I  am  before  it  is  at  London. 
Again,  suppose  I  sail  from  London  for  the  West  Indies. 
After  a  boisterous  passage,  during  which  no  observa- 
tions of  the  heavenly  bodies  could  be  taken,  and  it  was 
impossible  to  keep  the  ship's  reckoning,  I  fall  upon  a 
coast,  but  know  not  whether  it  be  that  of  an  island  or  of 
the  American  continent.     When  the  sun  is  in  the  meri- 
dian, I  find  by  my  watch,  that  it  is  a  trifle  more  than  7 
minutes  past  5  at  London.     By  turning  this  difference 
of  5  hours  7  minutes  into  degrees,  I  find  I  am  in  longi- 
tude about  76°  45^,  and  this  must  be  west,  because  it 
is  noon  where  I  am  later  than  at  London.     But  in  this 
case  when  I  have  found  my  longitude,  I  have  not  deter- 
mined the  coast.     For   by  reference  to  a  chart  or  a 
map,  I  find  I  may  be  either  on  the  coast  of  the  southern 
part  of   the   United   States,  of  the   Island   Cuba,   of 
Jamaica,  or  of  the  northern  coast  of  South  America. 
But  by  taking  the  sun's  altitude  at  the  same  time,  and 
thus  finding  my  latitude,  say  22°  30^  north,  I  ascertain 
which  of  these  several  coasts  I  am  on  ;  viz.  that  of  Cuba. 
77.  The  principal  difficulty  in  ascertaining  longitude 
by  this  method  is,- that  no  timepieces  have  yet  been 
constructed,    and   none    probably  can  be,  which  will 
measure  time  accurately,  and  without  variation.    Clocks, 
which  move  by  weights  and  are  regulated  by  pendu- 
lums, are  most  uniform  in  their  movements.     But  the 
constant  motion  of  the  vessel  entirely  precludes  their 
use  at  sea.     Incredible  pains  have  been  taken  to  ren- 
der watches  and  chronometers  accurate  measurers  of 


14.  Of  Latitude  and  Longitude. 

time  i  but  variation  in  the  temperature  of  the  air  ren- 
ders their  movements  more  or  less  irregular. 

It  is  not  always  necessary  to  wait  for  the  sun  to  come  to  the  meri- 
dian, in  order  to  know  the  time  of  day.  It  may  be  known  by  other 
ways,  as  by  the  rising  and  setting  of  the  sun,  and  of  stars  near  the 
equator. 

78.  Hence  it  is  often  desirable  to  correct  timepieces 
at  sea ;  and  for  this  purpose  eclipses  of  the  moon  are 
sometimes  of  use.  For  eclipses  of  the  moon  take  place 
at  precisely  the  same  time  to  all  to  whom  the  moon  is 
visible;  which  is  not  tiie  case  with  eclipses  of  the  sun, 
as  will  be  shown  hereafter,  /^hus,  if  I  sail  from  Lon- 
don, having  an  almanac  in  which  the  precise  time  of 
the  beginning  or  ending  of  a  lunar  eclipse  is  calculated 
for  the  time  at  London ;  if  the  moon  is  visible  to  me  at 
the  time  of  eclipse,  by  obsemng  the  time  of  its  begin- 
ning or  ending,  I  get  the  true  time  at  London,  and  can 
correct  my  timepiece  accordingly.  For  example,  if,  on 
a  particular  day,  an  eclipse  of  the  moon  is  calculated  to 
begin  at  17  minutes  past  11  in  the  evening,  London 
time,  and  at  f^ea  I  observe  it  begin  at  12  minutes  past 
1 1  by  my  chronometer,  I  know  the  chronometer  is  5 
minutes  too  slow,  that  is,  slower  than  London  time,  and 
[  can  correct  it  accordingly. 

Though  eclipses  of  the  moon  take  place  at  the  same  instant  to  all 
spectators,  it  is  difficult  to  tell  the  precise  moment  when  they  begin 
or  end,  as  will  be  explained  in  its  proper  place. 

79.  Hence  if  eclipses  were  frequent,  timepieces,  by 
being  often  regulated,  would  generally  show  correct 
time.  But  it  is  only  in  comparatively  few  voyages, 
during  his  life,  that  the  navigator  has  opportunity  of 
witnessing  a  lunar  eclipse.  On  this  account  astrono- 
mers have  turned  their  attention  to  the  eclipses  of  other 
bodies,  and  especially  to  those  of  the  satellites  of  Jupi- 
ter. These  eclipses,  like  those  of  the  moon,  take 
place  at  the  same  instant  to  all  spectators,  and  are  suf- 


Of  Latitude  and  Longitude,  45 

.         .         .  "^ 

ficiently  frequent  for  correcting  timepieces  at  sea,-^ 

there  being  scarcely  a  day,  during  which  one  or  more 
of  these  satelUtes  is  not  eclipsed.  But  at  present  it  ap- 
pears impossible  to  realize  the  peculiar  advantages, 
which  these  phenomena  are  calculated  to  afford.  (Fox 
the  satellites  of  Jupiter  are  too  small  to  be  visible  to  the 
naked  eye,  and  the  motion  of  the  vessel  renders  a  tele- 
scope useless..  Hence,  although  astronomers  have  ta- 
ken great  pains  to  calculate  these  eclipses,  yet  tliey 
seem  to  have  added  nothing  to  the  customary  means  of 
findino^  lonoitude  at  sea. 

80.  There  is  a  method  of  ascertaining  the  time  at 
London  by  observing  the  moon's  place.)  Tables  are 
calculated,  showing  the  distance  of  the  moon  from  the 
sun  and  some  fixed  stars  for  every  day  at  noon,  and 
every  three  hours  afterv/ards,  London  time.  To  ex- 
plain the  use  of  these  tables,  suppose  on  a  particular  day 
it  is  stated  in  them  that  the  moon  will  be  65^  eastward 
from  the  sun  at  6  o'clock  in  the  evening,  London  time. 
At  sea  I  observe  that  the  moon  is  not  65^  eastvv  ard  from 
the  sun  till  40  minutes  past  7,  by  the  time  where  I  am. 
This  difference  of  1  hour  40  minutes  gives  a  longitude 
of  25^ ;  and  this  must  be  eastward,  because  the  time 
where  I  am  is  later  than  that  at  London.  To  an  as- 
tronomer, accustomed  to  the  application  of  the  neces- 
sary principles,  this  method  of  finding  the  longitude 
would  be  the  most  accurate.  Tables  of  the  moon's 
parallax  have  been  lately  calculated ;  so  that  this  method 
of  finding  longitude  is  accommodated  to  the  capacity  of 
the  mass  of  navigators,  and  is  daily  coming  more  into 
use.  But  on  account  of  the  moon's  parallax,  which 
will  be  explained  hereafter,  it  has  hitherto  been  difficult 
to  apply  these  tables. 

8L  Notwithstanding  these  various  methods  of  finding; 
longitude,  it  is  still  very  difficult.  /"An  easy,  expeditious. 
and  sure  method  of  effecting  this  purpose  is  a  great 
5* 


46  Of  Latitude  and  Longitude, 

desideratvm.  Such  a  discovery  would  constitute  a  new 
era  in  navigation,  scarcely  less  important  than  that  of 
the  discovery  of  the  mariner's  compass.  The  English 
nation,  to  whom  every  facility  in  the  improvement  of 
commerce  is  particularly  important,  have  used  all  suita- 
ble means  to  direct  the  attention  of  astronomers  to  this 
subject.  By  an  act  of  parliament,  passed  1714,  the 
English  government  offered  20,000  pounds  reward  to 
any  person  who  should  discover  a  method  of  finding 
longitude  at  sea  within  30  miles,  or  J  a  degree  ;  15,000 
pounds,  if  within  40  miles,  or  |  of  a  degree  ;  and  10,000 
pounds,  if  within  60  miles,  or  a  degree.  Mr.  John  Har- 
rison, an  eminent  artist,  obtained,  at  two  different  times, 
20,000  pounds  for  improving  chronometers.  So  ex- 
act was  one  of  h'.s  construction,  that  it  erred  but  1  mi- 
nute 54  seconds  in  5  months,  a  mean  daily  error  of  | 
second.  By  a  new  act  of  parliament,  passed  1774, 
the  greatest  reward  which  can  now  be  obtained  is 
ri 0,000  pounds. 


Of  Latitude  and  Longitude.  A^ 


TABLE 

Shoidng  the  length  of  a  degree  of  Longitude  for  every 
degree  of  Latitude^  in  geographical  miles. 


ig.  Lat. 

Miles. 

Deg.  Lat. 

Miles. 

Deg.  Lat. 

Miles 

1 

59,96 

31 

51,43 

61 

29,04 

2 

59,94 

32 

50,88 

62 

28,17 

3 

59,92 

33 

50,32 

63 

27,24 

4 

59,86 

34 

49,74 

64 

26,30 

5 

59,77 

35 

49,15 

65 

25,36 

6 

59,67 

36 

48,o4 

66 

24,41 

7 

59,56 

37 

47,92 

67 

23,45 

8 

59,40 

38 

47,28  ■ 

68 

22,48 

9 

59,20 

39 

46,62 

69 

21,51 

10 

58,18 

40 

46,00 

70 

20.  ^i 

11 

58,89 

41 

45,28 

71 

1:^.54 

12 

?-£  1)8 

42 

44,95 

72 

18,55 

13 

58,46 

43 

43,88 

73 

17,5} 

14 

.'•.::i,22 

44 

43,16 

74 

16,53 

15 

58,00 

45 

42,43 

75 

15,52 

16 

57,60 

46 

41,68 

76 

14,51 

17 

57,30 

47 

41,00 

77 

13,50 

18 

57,04 

48 

40,15 

78 

12,48 

19 

56,73 

49 

39,36 

79 

11,45 

20 

56,38 

50 

38,57 

80 

10,42 

21 

56,00 

51 

37,73 

81 

09,38 

22 

55,63 

52 

37,00 

82 

08,35 

23 

55,23 

53 

36,18 

83 

07,32 

24 

54,81 

54 

35,26 

84 

06,28 

25 

54,38 

55 

34,41 

85 

05,23 

26 

54,00 

56 

33,55 

86 

04,18 

27 

53,44 

57 

32,67 

87 

03,14 

28 

53,00 

58 

31,70 

88 

02,09 

29 

52,48 

59 

30,90 

89 

01,05 

30 

51,96 

60 

30,00 

90 

00,00 

48      Apparent  Motions  and  Magnitudes  of  Planets.     -  ^ 

CHAP.  III. 

82.  In  the  short  account  given  of  the  solar  system  in 
Chap.  I,  we  attempted  to  describe  the  appearances  of 
the  various  heavenly  bodies,  and  to  state  such  facts  re- 
lating to.  theui,  as  are  known  to  exist.  But  there  are 
many  particular  appearances  and  phenomena  peculiar 
to  each  planet,  arising  from  its  situation  in  the  solar  sys- 
tem, from  its  revolution  on  its  avis,  from  its  revolution 
round  the  sun  together  with  the  degree  in  which  its  equa- 
tor varies  from  its  ecliptic,  (called  the  obliquity  of  the 
ecliptic,)  from  its  atmosphere,  and  from  its  size.  These 
phenomena  are  of  little  use  or  interest  to  us,  as  they 
affect  the  inhabitants  of  other  planets ;  but  are  of  great 
use  as  they  affect  us.  Hence  we  shall  confine  ourselves 
to  such  as  relate  to  the  earth,  and  are  of  constant  ob- 
servation. 

Sect.  I. 

Of  Phenomena  arising  from  the  situation  of  the  Earth 
in  the  Solar  System, 

Art.  1.  Of  the  different  apparent  motions  and  magnitudes 
of  the  other  planets, 
83.  The  primary  planets  seen  from  the  sun  always 
appear  to  move  the  same  way,  viz.  from  west  to  east, 
which  is  their  direct  motion.  But  as  seen  from  any 
planet,  all  the  rest  appear  to  move  from  west  to  east 
part  of  the  time,  to  be  stationary  part  of  the  time,  and 
to  move  from  east  to  west  part  of  the  time ;  (which  last 
is  called  retrograde  motion.  PI.  III.  fig.  3.)  Let  S 
be  the  sun,  E  the  earth,  and  a,  h,  c,  d,  e,f,  g,  h,  Venus 
in  difterent  points  in  her  orbit.  It  is  plain,  that  while 
Venus  is  passing  from  d  to  /,  it  will  appear  to  move 
in  the  starrv  heavens  in  the  direction  from  o  to  n,  whe- 


"    Apparent  Motions  and  Magnitudes  of  Planets.       40 

ther  seen  from  the  sun  or  the  earth  ;  consequently  its 
motion  will  be  direct.  "  But  while  it  is  passing  from  h  to 
I),  it  will  appear  to  move  from  m,  through  ti,  o,  to  p,  in 
a  different  direction,  as  seen  from  the  earth,:  from  that 
in  which  it  appears  to  move,  as  seen  from  the  sun  5,  that 
is,  its  motion  is  retrograde,  and  directly  contrary  to 
what  it  was  in  the  opposite  part  of  its  orbft^  While  it 
is  passing  from  b  to  c.  Or  from  g  to  A,  it  is  moving  al- 
most directly  from  or  to  the  eariii,  nnd  consequently  it 
will  appear  nearly  stationary  among  the  stars.  At  e 
Venus  is  said  to  be  in  its  superior  conjunction,  because 
it  is  beyond  the  sun ;  at  a  it  is  said  to  be  in  its  inferior 
conjunction,  because  it  is  between  the  sun  and  earth. 
The  motions  and  conjunctions  of  Mercury  are  like  those 
of  Venus. 

8^1  It  is  obvious  also,  that  while  the  motion  of  Venus 
is  direct  or  retrograde  to  us  on  earth,  the  motion  of  the 
earth  will  be  direct  or  retrograde  to  the  inhabitants  of 
Venus ;  for,  while  Venus  passes  from  h  to  &,  and  is  re- 
trograde to  us,  the  earth  appears  to  move  from  r  towards 
.s,  directly  opposite  to  its  motion  as  seen  from  the  sun. 
But  while  Venus  is  moving  from  d  to  /,  the  earth  will 
appear  to  move  in  the  same  direction  as  if  seen  from 
the  sun,  that  is,  from  v  towards  r.  So  also  while  Ve- 
nus appears  to  us  stationary  at  and  near  her  greatest 
elongation,  the  earth  appears  stationary  to  an  inhabitant 
of  Venus.  When  Venus  is  at  a,  the  earth  is  in  oppo- 
sition ;  that  is,  in  a  part  of  the  heavens  directly  opposite 
to  the  sun.  -  But  when  Venus  is  at  e,  the  earth  is  in  con- 
junction with  the  sun.  Now,  precisely  the  same  motions 
which  the  earth  exhibits  to  the  inhabitants  of  V^enus,  each 
of  the  exterior  planets  exhibits  to  us. 

85.  It  is  plain  also,  that  from  the  earth's  situation 
out  of  the  centre  of  the  solar  system,  the  apparent  mag- 
nitudes of  the  other  planets  vary  y  for  common  experi- 
ence shows,   that  as  objects   are   nearer  they  appear 


^m> 


So  Of  Eclipses. 

larger.  Hence,  when  Venus  is  nearest  the  earth,  as  at 
or  near  a,  its  magnitude  must  appear  larger,  than  when 
at  or  near  e.  As  the  apparent  magnitudes  of  other 
planets  vary  to  us,  that  of  the  earth  varies  to  them. 

Art.  2.     Of  Eclipses. 

86.  The  situation  of  the  earth  with  regard  to  the 
moon,  or  rather  of  the  moon  with  regard  to  the  earth, 
occasions  eclipses  both  of  the  sun  and  moon.  Those 
of  the  sun  take  place  when  the  moon,  passing  between 
the  sun  and  earth,  intercepts  his  rays.  Those  of  the 
moon  take  place  when  the  earth,  coming  between  the 
sun  and  moon,  deprive  the  moon  of  his  light.  Hence 
an  eclipse  of  the  sun  can  take  place  only  when  the  moon 
changes,  and  an  eclipse  of  the  moon  only  when  the 
moon  fulls ;  for  at  the  time  of  an  eclipse,  either  of  the 
sun  or  moon,  the  sun,  earth,  and  moon  must  be  in  the  same 
straight  line. 

87.  If  the  moon  went  round  the  earth  in  the  same 
plane  in  which  the  earth  goes  round  the  sun,  that  is, 
in  the  ecliptic,  it  is  plain  that  the  sun  would  be  eclipsed 
at  every  new  moon ;  and  the  moon  would  be  eclipsed 
at  every  full.  For  at  each  of  these  times,  these  three 
bodies  would  be  in  the  same  straight  line.  'But  the 
moon's  orbit  does  not  coincide  with  the  ecliptic,  but  is 
inclined  to  it  at  an  angle  of  about  5^  20^  Hence,  since 
the  apparent  diameter  of  the  sun  is  but  about  J  a  degree, 
and  that  of  the  moon  about  the  same,  no  eclipse  will 
take  place  at  new  or  full  moon,  ^nless  the  moon  be 
within  ^  a  degree  of  the  ecliptic,  that  is,  in  or  near  one 
of  its  nodes.  It  is  found  that  if  the  moon  be  within 
16J°  of  a  node  at  time  of  change,  it  will  be  so  near  the 
ecliptic,  that  the  sun  will  be  more  or  less  eclipsed  ;  if 
within  12^  at  time  of  full,  the  moon  will  be  more  or 
less  eclipsed. 


Of  Eclipses.  51 

88.  It  is  obvious  that  the  moon  will  be  oftener  within 
16J^  of  a  node  at  the  time  of  change,  than  within  12^  at 
the  time  of  full ;  consequently  there  will  be  more  eclip- 
ses of  the  sun  than  of  the  moon  in  a  course  of  years. 
As  the  nodes  commonly  come  between  the  sun  and 
earth  but  twice  in  a  year,  and  the  moon's  orbit  contains 
360^5  of  which  .16^^,  the  limit  of  solar  eclipses,  and 
12^,  the  limit  of  lunar  eclipses,  are  but  small  portions, 
it  is  plain  there  must  be  many  new  and  full  moons  with- 
out any  eclipses. 

89.  Although  there  are  more  eclipses  of  the  sun  than 
of  the  moon,  yet  more  eclipses  of  the  moon  will  be  vi- 
sible at  a  particular  place,  as  Boston,  in  a  course  of  years, 
than  of  the  sun.  Since  the  sun  is  very  much  larger 
than  either  the  earth  or  moon,  the  shadow  of  these  bo- 
dies must  always  terminate  in  a  point ;  that  is,  it  must 
always  be  a  cone.  (See  PI.  IV.  fig.  1  and  2.)  Let  S 
be  the  sun,  m  the  moon,  and  E  the  earth.  The  sun 
constantly  illuminates  half  the  earth's  surface,  that  is,  a 
hemisphere ;  and  consequently  he  is  visible  to  all  in 
this  hemisphere.  But  the  moon's  shadow  falls  upon 
but  a  part  of.  this  hemisphere  ;  and  hence  the  sun  ap- 
pears eclipsed  to  but  a  part  of  those  to  whom  he  is  vi- 
sible. (^Sometimes  when  the  moon  is  at  its  greatest  dis- 
tance, its  shadow  o  m,  terminates  before  it  reaches  the 
earth>  In  eclipses  of  this  kind,  to  an  inhabitant  directly 
under  the  point  o,  the  outermost  edge  of  the  sun's  disk 
is  seen,  forming  a  bright  ring  round  the  moon ;  from 
which  circumstance  these  eclipses  are  called  annular, 
from  annulus,  a  Latin  word  for  ring. 

90.  Besides  the  dark  shadow  of  the  moon  m  o,  in 
which  all  the  light  of  the  sun  is  intercepted,  (in  which 
case  the  eclipse  is  called  total,)  there  is  another  shadow 
r  CDs,  distinct  from  the  former,  which  is  called  the  ^e- 
numbra.  i  Within  this,  only  a  part  of  the  sun's  rays  are 
intercepted,  and  the  eclipse  is  called  partial.     If  a  per- 


52  Of  Eclipses. 

son  could  pass,  during  an  eclipse  of  the  sun  from  o  to 
D,  inmiedl_:tely  on  immerging  from  the  dark  shadow 
0  m,  he  would  see  a  small  part  of  the  sun ;  and  would 
continually  see  more  and  more  till  he  arrived  at  JD, 
where  all  shadow  would  cease,  and  the  whole  sun's  disk 
be  visible.  Appearances  would  be  similar  if  he  w^ent 
from  0  to  C.  Hence  the  penumbra  is  less  and  less  dark, 
(because  a  less^  portion  of  the  sun  is  eclipsed,)  in  pro- 
portion as  the  spectator  is  more  remote  from  o,  and 
nearer  C  or  D.  Though  the  penumbra  is  continually 
increasing  in  diameter  according  to  its  length,  or  the 
distance  of  the  moon  from  the  earth,  still,  under  the 
most  favourable  circumstances,  it  falls  on  but  about  half 
of  the  illuminated  hemisphere  of  the  earth,  (llence  by 
half  the  inhabitants  on  this  hemisphere  no.  eclipse  wdll 
be  seen. 

91.  But  the  case  is  different  in  eclipses  of  the  moon. 
(Fig.  2.)  fThe  instant  the  moon  enters  the  earth's 
shadow  at  x,  it  is  deprived  of  the  sun's  light,  and  is 
eclipsed  to  all  in  the  unilluminated  hemisphere  of  the 
earth.  Hence  eclipses  of  the  moon  are  visible  to  at 
least  twice  as  many  inhabitants  as  those  of  the  sun  can 
be ;  generally  the  proportion  is  much  greater^  Thus 
the  inhabitants  at  a  particular  place,  as  Boston,  see 
more  eclipses  of  the  moon  than  of  the  sun. 

92.  The  reason  why  a  luna?-  eclipse  is  visible  to  all 
to  whom  the  moon  at  the  time  is  visible,  and  a  solar 
one  is  not  to  all  to  whom  the  sun  at  the  time  is  visible, 
may  be  seen  from  the  nature  of  these  eclipses.  We 
speak  of  the  sun's  being  eclipsed  ;  but  properly  it  is  the 
earth  which  is  eclipsed.  No  change  takes  place  in  the 
sun ;  if  there  were,  it  would  be  seen  by  all  to  whom 
the  sun  is  visible.  But  he  continues  to  diifuse  his  beams 
as  freely  and  uniformly  at  such  times  as  at  others.  But 
these  beams  are  intercepted,  and  the  earth  is  eclipsed ; 
but  only  where  the  moon's  shadow  falls,  that  is,  on  only 


Of  Eclipse,^  53 

a  part  of  a  nermsphere.  But  in  eclipses  of  the  moon, 
that  body  ceases  to  receive  hght  from  the  sun,  and  con- 
sequently ceases  to  reflect  it  to  the  earth.  The  moon 
undergoes  a  change  in  its  appearance  ;  and  consequent- 
ly this  change  is  visible  at  the  same  time  to  all  to  v/hom 
the  moon  is  visible ;  that  is,  to  a  whole  hemisphere  of 
the  earth. 

93.  The  earth's  shadow  (like  that  of  the  moon)  is 
encompassed  by  a  penumbra  C  r  s  jD,  which  is  faint  at 
the  edges  towards  r  and  5,  but  becomes  darker  towards 
F  and  G,  The  shadow  of  the  earth  is  but  little  darker 
than  the  region  of  the  penumbra  next  to  it.  Hence  it 
is  very  difficult  to  determine  the  exact  time  when  the 
moon  passes  from  the  penumbra  into  the  shadow,  and 
from  the  shadow  into  the  penumbra  ;  that  is,  when  the 
eclipse  begins  and  ends.  But  the  beginning  and  en*d- 
ing  of  a  solar  eclipse  may  be  determined  instantane- 
ously. 

94.  The  shadows  of  all  the  planets  (like  those  of  the 
earth  and  moon)  terminate  in  a  point ;  and  this  point  is 
always  so  near  the  body,  that  one  primary  planet  can 
in  no  case  enter  into  the  dark  shadow^  of  another.  But 
their  penumbras  continually  become  broader  ;  and  con- 
sequently one  primary  planet  often  passes  through  the 
penumbra  of  another.  But  the  penumbra  of  the  earth 
is  so  faint,  that  the  passage  of  a  superior  planet  through 
it  is  not  perceptible  to  us. 

95.  Let  S  (PI.  IV,  fig.  3,)  be  the  sun,  E  the  earth 
surrounded  by  the  moon's  orbit ;  let  JVO  be  the  moon's 
nodes.  It  is  plain  that  if  the  moon's  nodes  were  always 
in  the  same  places,  each  of  them  would  be  between  the 
earth  and  sun  once  a  year,)  or  while  the  earth  is  revolv- 
ing round  the  sun.  For  example,  the  node  O  is  thus 
situated  in  the  figure,  and  the  node  JV*  would  be,  when 
the  earth  comes  into  the  directly  opposite  point  of  its 
orbit.     JVoiv  there  must  be  an  eclipse  of  the  sun  as  often 

6 


54  Of  EcItp.os. 

at  least  as  one  of  the  moon''s  nodes  eomes  between  the  sun 
and  eartlu  For  it  has  been  stated,  that  if  the  moon  be 
within  iG^o  ^^f  ^^  ^^^^^^  ^g  q^  .^^  ^1^^  ^-^^^  ^^  change,  the 
sun  will  be  eclipsed.  That  is,  there  are  (IGiX-^)  33^ 
between  1  and  2,  within  which  if  tlie  moon  be,  at  the 
time  of  change,  the  sun  will  be  eclipsed.  Now  the 
earth  moves  round  the  sun,  and  causes  the  sun  to  appear 
to  move  round  the  earth  (3()CP)  in  about  365  days;  that 
is,  through  little  less  than  F  in  one  day.  Consequent- 
ly the  sun  would  be  little  more  than  33  days  in  passing 
(apparently)  through  33^  of  the  ecliptic,  equal  to  33^  of 
the  moon's  orbit,  or  the  distance  from  1  to  2.  But  the 
moon. is  only  29 i  days  in  passing  from  one  change  to 
another  ;  so  that  the  moon  must  always  be  at  least  once 
(it  may  be  twice)  between  1  and  2,  while  the  sun  iis 
passing  dnough  the  corresponding  33^  of  the  ecliptic. 
Hence,  were  the  nodes  stationary,  there  would  always 
be  at  least  two  solar  eclipses  every  year. 

06.  But  there  may  not  be  any  eclipses  of  the  moon 
during  a  year.  For  the  shadow  of  the  earth  at  JS\  be- 
tween 1  and  2,  falls  upon  the  moon  only  when  the  moon 
is  in  a  space  of  24^  (12^  each  side  of  the  node)  of  the 
moon's  orbit.  And  as  the  moon  does  not  complete  its 
revolution  in  24  days,  it  may  not  necessarily  be  between 
1  and  2  w  hile  the  sun  is  passing  through  24^  in  tlie  op- 
posite part  of  the  ecliptic. 

97.  The  moon's  nodes  are  not  stationary,  but  move 
backwards  from  east  to  west.  So  that  if  the  node  be  at 
O  at  one  change,  it  will  be  someuhere  at  1  the  next. 
Hence  in  some  years  a  node  is  between  the  sun  and 
earth  three  times.  But  this  motion  of  the  nodes  is  so 
slow,  that  they  complete  their  revolution  in  but  little 
less  than  19  years.  Thus  generally  w^e  have  two  solar 
eclipses  in  a  year,  sometimes  three  or  four.;  The  great- 
est number  of  both  solar  and  lunar  eclipses,  that  can 
take  place  in  a  year,  is  seven      The  most  usual  nun)- 


Of  Eclipses.  55 

ber  is  four ;  two  solar,  and  two  lunar.  When  seven 
eclipses  take  place  in  a  year,  a  node  is  three  times  be- 
tween the  sun  and  earth. 

98.  The  diameters  of  the  sun  and  moon  are  supposed 
to  be  divided  into  12  equal  parts  called  digits.  These 
bodies  are  said  to  have  as  many  digits  eclipsed,  as  there 
are  of  those  parts  involved  in  darkness. 

Among  the  ancients,  eclipses  were  regarded  much  in  the  same 
light  that  comets  were,  as  alarming  deviations  from  the  established 
laws  of  nature,  totally  unaccountable,  and  presaging  direful  cala- 
mity to  individuals  or  to  the  State,  in  Fergusons  Astronomy,  No. 
328,  is  a  short  list  of  eclipses  ard  remarkable  historical  events, 
which  happened  about  the  same  time.  A  few  philosophers  arose  at 
intervals,  vvho  were  able  to  penetrate  the  cause  of  these  phenomena, 
and  even  to  predict  their  return.  But  these  were  few,  and  did  lit- 
tle or  notiiing  towards  enlightening  their  countrymen  on  these  sub- 
jects. Genius  and  skill  were  put  in  requisition  to  search  out  the 
regions  and  8!ibj*?cts  ai^ainst  which  the  malevolent  effects  of  a  par- 
ticular eclipse  were  aimed.  Treatises  were  written  to  show,  that  the 
effects  of  an  eclipse  of  the  sun  continued  as  many  years  as  the  eclipse 
lasted  hours  ;  and  th;it  of  the  moon  as  many  months. 

A  total  eclipse  of  the  sun  is  a  very  curious  and  rare  spectacle. 
Clavius  observed  one  at  Coimbra,  in  Portugal,  August  21,  1560. 
He  observes,  that  the  obscurity  was  more  striking  and  sensible  than 
that  of  night.  It  was  so  dark  for  some  time,  that  he  could  scarcely 
see  his  hand  ;  some  af  the  largest  stars  made  their  appearance  for 
a  minute  or  two,  and  the  birds  were  greatly  terrified. 

.June  1(),  1806,  a  very  remarkable  total  eclipse  took  place  at  Bos- 
ton. The  day  was  clear,  pnd  nothing  occurred  to  prevent  accurate 
obvervation  of  this  interesting  phenomenon.  Several  stars  were 
visible  ;  the  birds  were  greatly  agitated  ;  a  gloom  spread  over  the 
landscape,  and  an  indescribable  sensation  of  fear  or  dread  pervaded 
the  breasts  of  those,  who  gave  themselves  up  to  the  simple  effects 
of  the  phenomenon,  without  having  their  attention  diverted  by  ef- 
forts of  observation.  The  first  gleam  of  light,  contrasted  with  the 
previous  darkness,  seemed  like  the  usual  meridian  day,  and  gave 
indescribable  life  and  joy  to  the  whole  creation.  Tt  is  to  be  doubt- 
ed if  there  was  a  single  person  gazing  at  the  sun,  or  rather  the  moon, 
at  that  moment,  who  did  not  feel  relieved  from  an  uneasy  sensation, 
and  betray  that  relief  in  the  instantaneous  subsequent  cheerfulness 
of  his  countenance.  A  total  eclipse  of  the  sun  can  last  but  little 
more  than  three  minutes.  An  annular  eclipse  of  the  sun  is  still  more 
rar3  than  a  total  one. 


56  Day  and  JVignt. 

Sect.  II. 

Of  Phenomena  arising  from  the  Revolution  of  the  Earth 
on  its  ovm  aans. 

DAY  AND  NIGHT. 

99.  Common  experience  shows,  that  when  we  are 
moving  swiftly  in  one  direction,  surrounding  objects 
appear  to  be  moving  in  the  opposite  direction.  This 
effect  is  no  where  more  striking  than  in  sailing  near  a 
shore  or  coast.  It  is  difficult  for  a  person  in  this  situa- 
tion for  the  first  time,  to  realize  that  himself,  and  not 
the  land,  is  in  motion.  So  by  the  earth's  motion  on  its 
axis  from  west  to  east,  the  sun  and  stars  appear  to  move 
from  east  to  west.  The  sun  constantly  shines  upon 
one  half  the  earth's  surface ;  and  by  the  regular  motion 
of  the  earth  on  its  axis,  every  place  is  successively 
brought  into  light  and  immersed  in  darkness.  This 
occasion?  alternate  day  and  night. 

100.  If  the  line  KS  (PI.  IV,  fig.  4,)  about  which  the 
earth  turns,  were  always  in  the  circle  dividing  the  light 
from  the  dark  hemisphere,  the  days  would  every  where 
be  of  the  same  length,  and  just  as  long  as  the  nights. 
For  an  inhabitant  at  the  equator,  at  o,  and  one  on  the 
sanie  meridian  towards  the  poles,  as  at  /,  would  come 
into  the  light  at  the  same  time,  would  com.e  to  the  me- 
ridian r  Q,  at  the  same  time,  and,  on  the  other  side, 
would  immerge  into  darkness  at  the  same  time.  And 
since  the  motion  of  the  earth  is  uniform,  they  would  be 
in  the  dark  hemisphere  just  as  long  as  in  the  light;  that 
is,  the  night  would  be  just  as  long  as  the  day. 

101.  But  this  is  not  the  position  of  the  line  AIS,  ex- 
cept when  the  sun  is  in  the  celestial  equator.  But  as 
the  ecliptic  and  the  equator  make  an  angle  with  each 
other  of  23.p,  the  sun  cannot  be  in  the  celestial  equa- 
tor, except  at  the  points  where  the  equator  cuts  the 


Day  and  JVight,  57 

ecliptic,  which  are  the  beginning  of  the  signs  Aries  and 
Libra.  The  sun  enters  these  signs  on  the  20th  March 
and  23d  of  September.  Hence  at  these  periods,  and 
at  no  others,  the  days  and  nights  are  equal  all  over  the 
world  ;  and  on  this  account  they  are  d^Wed  equinoxes  ; 
the  first  the  vernal  equinox,  the  second  the  autumnal. 
At  these  seasons,  the  sun  rises  exactly  in  the  east  at  6 
o'clock,  and  sets  exactly  in  the  west  at  6  o'clock. 

102.  But  at  other  seasons,  when  the  sun  is  not  in 
the  celestial  equator,  the  line  JSTS  is  not  in  the  circle  di- 
viding the  light  from  the  dark  hemisphere  ;  but  has  more 
or  less  of  the  position  as  represented  at  sign  Cancer  (^) 
or  Capricorn  (Vj).  (PI.  V,  fig.  1.)  Here  it  is  plain 
that  an  inhabitant  at  the  equator  o,  does  not  come  out 
of  the  dark  hemisphere,  or  immerge  into  it,  at  the  same 
time  with  an  inhabitant  on  the  same  meridian  towards 
the  poles  as  at  /.  But  while  the  earth  is  at  Vy,  an  in- 
habitant at  /is  in  the  light  hemisphere  longer  than  in 
the  dark ;  that  is,  the  day  is  longer  than  the  night.  But 
at  Z5,  an  inhabitant  at /is  in  the  dark  hemisphere  long- 
er than  in  the  light.  Whereas  in  all  situations  of  the 
earth,  day  and  night  are  equal  at  the  equator. 

10^.  It  is  plain  from  these  figures,  that  when  the  days 
are  longest  in  north  latitude,  they  are  shortest  in  south 
latitude,  and  vice  versa^  It  is  also  plain,  that  as  the  sun 
has  declination  from  the  celestial  equator  either  north 
or  south,  he  shines  over  or  beyond  one  pole,  and  not 
to  the  other.  So  that  there  is  a  region  about  one  pole, 
w^ich  is  a  long  time  in  the  light  hemisphere  ;  and  a  re- 
gion about  the  other  pole,  which  for  an  equal  leng'.h  of 
time  is  in  the  dark  hemisphere.  At  the  poles,  there  is 
but  one  day  and  one  night  in  a  year,  each  of  six  months. 
The  distance  to  which  the  sun  shines  beyond  the  poles 
is  always  equal  to  his  own  declination ;  and  as  his  de- 
clination can  be  but  23J^y  he  can  never  shine  but  23^^ 
beyond  a  pole.     Less  circles  surrounding  the  eartii  »* 


5S  Day  and  .Yight. 

the  distance  of  22^^  from  the  poles  are  called  polar 
circles.  Less  circles  surrounding  the  earth  at  the  dis- 
tance of  2o.]^  from  the  equator  are  called  tropics  ;  the 
one  on  the  north  side,  the  tropic  of  Cancer;  the  one  on 
the  south  side,  the  tropic  of  Capricorn, 

These  terms  are  indiscriminately  applied  to  these  circles,  as  drawn 
on  the  earth,' or  in  the  heavens.  The  subject  will  show  which  are 
meant. 

104.  When  the  sun  enters  the  signs  Zo  and  VJ,  (which 
takes  place  June  21,  and  December  22)  he  is  at  his 
greatest  declination,  and  in  the  tropics.  At  the  first 
period,  which  is  called  the  summer  solstice,  days  are 
longest  and  nights  shortest  in  north  latitude ;  and  nights 
longest  and  days  shortest  in  south  latitude.  At^the  lat- 
ter period,  which  is  called  the  iiinter  solstice,  directly 
the  reverse  is  the  case  in  each  latitude. 

105.  During  a  year  the  earth  turns  on  its  axis  once 
more  than  we  have  days.  The  reason  of  this  is,  that  on 
account  of  the  earth's  motion  in  her  orbit,  she  turns  a 
little  more  than  once  on  her  axis  between  the  time  of 
noon  one  day,  and  noon  the  next  day.  For,  (PL  V,  fig.  2,) 
if  the  earth  be  supposed  at  A  on  any  particular  day, 
and  the  place  e  be  under  the  sun  at  noon,  it  is  manifest 
that  on  the  next  day,  w^hen  the  earth  comes  to  B,  the 
place  e  will  not  be  under  the  sun,  when  it  has  com- 
pleted its  revolution ;  but  the  earth  must  revolve  through 
the  space  e  o,  before  it  is  noon  at  e.  So  again  on  the 
next  day,  when  the  earth  is  at  C,  the  earth  must  more 
than  complete  a  second  revoKition  by  the  space  eo,  be- 
fore it  is  noon  at  e.  These  little  excesses  amount  to  a 
whole  revolution  of  the  earth  on  its  axis  in  the  course 
c  f  a  year.  A  complete  revolution  of  the  earth  on  its 
a^is  constitutes  a  szWrnW  day ;  the  time  from  noon  to 
noon  constitutes  a  solar  or  natural  day.  Siderial  days 
are  all  of  the  same   lengtli^    but   solar   days  are  not. 


^bermtion  of  lAght,  59 

The  mean  difference  in  the  length  of  a  siderial  and 
solar  day  is  3^  56^^  The  cause  of  the  di  tie  rent  lengths 
of  solar  or  natural  days  will  be  explained,  when  we 
treat  of  equation  of  time. 

For  precisely  the  same  reason  that  the  earth  turns  on  its  axis  onr=' 
more  in  a  year,  than  there  are  solar  days,  the  moon  must  revolve 
once  more  round  the  earth,  than  it  changes  or  fulls,  in  the  course  of 
a  year.  For  between  one  change  and  another,  the  earth  has  advanc- 
ed  in  her  orbit ;  and  consequently  the  moon  must  more  than  complete 
her  revolution  before  she  can  be  between  the  sun  and  earth.  The 
time  she  occupies  in  describing  her  orbit  is  the  time  of  her  periodical 
revolution  ;  and  the  time  between  one  change  and  another,  or  one 
full  moon  and  another,  is  the  period 'of  her  Synodical  revolution. 


Sect.  III. 

Of  Phenomena  arising  from  the  Earth'' s  motion  round  the 
Sun,  together  loith  the  obliquity  of  the  Ecliptic, 

Art.  1.     Aberration  of  Light. 

106.  It  was  stated  above,  (No.  30,)  that  light  is  pro- 
gressive ;  that  it  is  not  transmitted  from  one  body  to 
another  instantaneously.  It  is  about  sixteen  minutes  in 
crossing  the  earth's  orbit :  that  is,  it  moves  at  the  rate 
of  about  200,000  miles  a  second.  The  earth  also 
moves  in  its  orbit  at  the  rate  of  about  68,000  miles  an 
hour;  that  is,  nearly  19  miles  a  second.  On  account 
of  these  two  motions,  viz.  of  light  and  of  the  earth,  we 
never  see  any  of  the  heavenly  bodies,  especially  the 
stars,  in  precisely  the  place  they  occupy,  but  a  little  to 
the  eastward  of  their  true  places. 

107.  To  illustrate  this,  (PI.  V,  fig.  3,)  suppose  light 
falling  upon  the  earth  at  a  from  a  star  in  the  line  a  c. 
Were  the  earth  stationary  at  a,  the  star  would  be  seen 
by  the  direct  ray  c  a,  and  would  appear  to  be  where  it 
actually  is.     But  while  the  direct  ray  c  «  is  coming  to 


60  ^lie  Seasons, 

the  earth,  the  earth  has  moved  from  a  to  h;  conse- 
OjUently,  the  star  will  not  be  seen  by  the  ray  c  «,  but  by 
the  ray  cb ;  and  this  in  the  direction  h  rf,  parallel  to 
a  c.  Hence  the  star  appears  at  rf,  instead  of  at  c.  This 
effect  is  called  the  aberration  of  light,  and  amounts  to 
about  2C  of  a  degree. 

If  the  pupil  find  the  preceding  illustration  difficult  to  be  under- 
stood, it  may  perhaps  be  rendered  more  intelligible,  if  we  suppose 
the  line  a  c  to  be  a  long  tube  or  telescope,  fixed  on  the  earth  in  the 
direction  represented  in  the  figure.  It  is  obvious  that  if  a  star  be 
seen  through  this  tube  or  telescope,  it  must  be  seen  at  that  place  ex- 
actly to  which  the  tube  or  telesct)pe  points.  Let  us  suppose  that  a 
ray  of  light  would  come  from  c  to  the  earth  in  the  same  time  that 
the  earth  v/ould  move  from  a  to  b.  If  the  ray  should  enter  the  tube 
or  telescope  in  a  direction  towards  a,  it  is  obvious  that  on  account  of 
♦.>e  motion  of  the  telescope,  the  ray  must  strike  upon  its  upper  side 
and  be  lost  before  it  comes  to  a.  But  if  the  ray  enter  at  c,  in  the  di- 
rection towards  h,  then  the  motion  of  the  telescope  will  prevent  it 
from  striking  its  under  side  ;  for  this  is  continually  sliding,  as  it  were, 
from  under  the  ray,  till  the  ray  reaches  b.  But  when  the  ray  reaches 
b,  the  telescope  is  in  the  position  b  rf,  and  the  eye  looking  through  the 
telescope  must  of  course  sec  the  star  at  d.  Now  the  effect  is  just 
the  same  on  the  naked  eye^  as  it  would  be  through  a  telescope. 


Art.  2.      The  Seasons. 

108.  As  the  earth's  orbit  is  elliptical,  the  earth  must 
at  one  season  of  the  year  be  nearer  the  sun,  than  at  an- 
other. For  instance  (PI.  I,  fig.  1,)  the  earth  is  nearer 
the  sun  at  A,  than  when  in  the  opposite  point  of  its 
orbit  at  C.  And  as  the  heat  and  light  from  the  sun 
are  greater  as  the  distance  is  less,  it  is  plain  the  earth 
must  receive  a  greater  degree  when  at  A,  than  when  at 
C.  This  circumstance  would  occasion  a  variation  in 
the  temperature  of  the  air,  analogous  to  the  seasons, 
were  the  sun  always  in  the  celestial  equator ;  that  is,  if 
the  equator  coincided  with  the  ecliptic.  But  the  sea- 
:sans  with  us,  in  north  latitude,  are  not  in  the  least  de- 


The  Seasons,  81 

gree  occasioned  by  this  circumstance.  For  the  earth 
is  nearest  to  the  sun  about  the  time  of  the  winter  sol- 
stice (22  December),  and  farthest  from  him  about  the 
time  of  the  summer  solstice,  (21  June). 

109.  But  our  seasons  are  occasioned  by  the  direction 
in  which  the  sun's  rays  fall  upon  us.  When  they  fall 
perpendicularly,  or  nearest  so,  the  season  is  warmest ; 
and  when  they  fall  most  obliquely,  or  in  a  slanting  man 
ner,  the  season  is  coldest.  For  (PI.  IV,  fig.  5,)  a  much 
smaller  portion  of  uinter  rays  fall  upon  a  given  surface, 
as  about  Boston,  than  of  summer  rays.  The  cause  of 
this  difference  in  the  obliquity  of  the  sun's  rays  is  the 
obliquity  of  the  ecliptic. 

110.  When  the  sun  is  in  the  celestial  equator,  (PL 
IV,  fig.  4,)  which  is  the  case  at  the  equinoxes,  when  he 
enters  the  signs  Aries  (<Y* )  and  Libra  (:£b),  and  the  earth 
enters  £1  and  «Y^,  the  sun's  rays  fall  perpendicularly  at 
the  equator,  and  with  equal  obliquity  in  north  and  south 
latitude  to  equal  distances  from  the  equator.  (PI.  V 
fig.  1.)  But  while  the  earth  moves  from  £1  to  Vy,  and 
the  sun  appears  to  move  from  of  to  25,  (which  is  done 
between  March  20  and  June  21,)  the  sun  appears  to 
recede  gradually  from  the  equator,  and  have  a  north 
declination.  During  this  period,  the  sun's  rays  do  not 
fall  perpendicularly  at  the  equator,  but  at  a  region  north 
of  the  equator,  and  less  obliquely  in  north  latitude  than 
iji  south  latitude.  Consequently  the  season  is  warmer 
in  north  latitude  than  in  south.  At  the  summer  solstice 
(June  21)  these  effects  are  greatest.  From  June  21  to 
September  22,  while  the  sun  appears  to  move  from  £5 
to  d2h,  he  seems  to  approach  the  celestial  equator,  and 
actually  comes  to  it  September  22,  when  the  rays  fall 
with  equal  obliquity  in  both  latitudes. 

111.  But  while  the  earth  passes  from  of  to  Z5,  and 
ttie  sun  from  £1  to  VJ ,  the  sun's  south  declination  gra- 
dually increases ;  his  rays  fall  perpendicularly  on  a  re- 


62  The  Seasons, 

gion  south  of  the  equator,  and  less  obliquely  in  south 
latitude  than  in  north.  Hence  at  this  period  (Decem- 
ber 22)  it  is  summer  in  south  latitude,  and  winter  in 
north.  For  this  situation  the  sun  gradually  returns  to 
the  equator,  where  he  arrives  at  the  vernal  equinox, 
March  20. 

112.  It  may  be  seen  by  the  figures,  that  at  the  same 
time  that  the  sun's  rays  are  nearest  perpendicular  at 
any  place,  the  days  are  also  longest,  whether  in  north 
or  south  latitude.  This  circumstance  contributes  much 
to  the  warmth  of  summer  and  the  cold  of  winter. 

113.  Since  the  degree  of  heat  from  the  sun  increases 
as  the  earth's  distance  decreases,  and  this  distance  is 
least  Xvhen  it  is  summer  in  south  latitude,  and  greatest 
when  it  is  summer  in  north  latitude,  it  follows,  that  a 
greater  degree  of  heat  is  received  in  summer  in  south 
latitude,  than  in  summer  in  north  latitude.  From  this 
circumstance,  w^e  might  be  led  to  suppose,  that  south 
latitude  is  most  favourable  to  veiretation.  But  to  com- 
pensate  for  a  less  degree  of  heat,  the  inhabitants  in  north 
latitude  have  longer  summers  than  those  in  south  lati- 
tude. For,  by  inspecting  the  figure,  as  the  sun  is  not 
in  the  centre  of  the  ellipse  but  in  a  focus,  the  earth  must 
pass  farther  in  going  one  half  its  orbit,  than  in  going  the 
other  half.  The  earth  also  moves  slower  as  it  is  farther 
from  the  sun.  Hence  it  occupies  a  longer  time  in  mov- 
ing through  one  half  its  orbit,  than  through  the  other. 
For  example,  the  earth  in  longer  in  passing  from  ^^^ 
through  Vy  to  Of ,  than  in  passing  from  <>f ,  through  £5 
to  £:=.  There  are  found  to  be  8  days  more  betw^een 
the  vernal  and  autumnal  equinoxes,  than  between  the , 
autumnal  and  vernal;  that  is,  our  summers  areiSdavsj 
longer  than  in  south  latitude. 

114.  Though  the  sun's  rays  fa?l  nearest  perpendicu- 
larly upon  us  in  north  latitude,  and  the  days  are  longest 
at  the  summer  solstice,  (June  21, J  and  most  obliquely, 


Equation  of  Timr  63 

and  the  days  are  shortest  at  the  winter  solstice,  (Decem- 
ber 22,j  yet  the  former  is  not  the  time  of  the  greatest 
warmth,  nor  the  latter  of  the  greatest  cold.  For  the 
atmosphere  derives  heat,  by  coming  in  contact  with  the 
earth.  So  that  when  the  earth  is  warmest,  the  atmo- 
sphere is  warmest,  and  when  the  earth  is  coldest,  the 
atmosphere  is  coldest.  But  the  earth  continues  to  ac- 
cumulate heat  for  some  time  after  the  sun's  rays  are 
most  powerful ;  and,  like  a  heated  ball,  is  not  divested 
of  it  till  after  the  period  when  the  sun's  rays  are  least 
powerful.  Hence  we  have  the  warmest  weather  in  the 
latter(part  of  July,  and  in  the  first  of  August;  and  our 
coldest  month  is  January.-  For  precisely ^he  same  rea- 
son, our  warmest  part  of  the  day  is  about/p  or  3  o^clock 
in  the  afternoon.\ 

115.  There  is  a  difference  between  a  solar  and  side- 
rial  year.  A  solar  year  is  the  time  in  which  the  earth 
passes  from  any  point  in  the  ecliptic,  as  the  beginning 
of  Aries,  to  the  same  point  again  ;  which  is  a  little  less 
than  a  complete  revolution,  as  will  be  explained  when 
we  treat  of  the  precession  of  the  equinoxes.  A  siderial 
year  is  the  time  of  performing  a  complete  revolution. 


Art.  3.     Equation  of  Time. 

116.  The  medium  length  of  a  solar  or  natural  day  is 
divided  into  24  equal  parts,  called  hours  ;  which  parts 
are  measured  by  correct  time-pieces.  But,  as  was 
stated  above  (105),  these  days  are  not  all  of  the  same 
length.  Hence  some  must  consist  of  more  and  some 
of  less  than  24  hours.  ^^When  a  natural  day  consists  of 
more  than  24  hours,  itls  plain  that  it  will  not  be  noon 
by  the  sun  till  it  is  past  noon  by  the  clock ;  in  which 
case  the  sun  is  said  to  be  slow  of  the  clock.  (When 
a  natural  day  consists  of  less  than  24  hours,  it  is  noon 


64  Equation  of  Time. 

by  the  sun  before  it  is  by  the  clock ;  in  v^^hich  case  the 
sun  is  said  to  be  faM  of  the  clock.  Time  measured  by 
a  clock  is  called  mean  time  ;  that  indicated  by  the  sun, 
or  shadow  on  a  common  dial,  is  called  apparent  time  ; 
'  and  the  difference  between  them  is  the  equation. 

117.  There  are  two  causes  of  the  inequality  of  na- 
tural days.  The  first  is,  that  the  eartKs  orbit  is  not  a 
circle,  hut  an  ellipse.      It  was  ascertained   by  Kepler, 

I  that  if  a  line  were  drawn  from  the  sun  to  the  earth,  this 
line  would,  by  the  earth's  motion,  pass  over  equal 
spaces,  or  areas,  in  equal  times.  If  then  the  distance 
of  the  earth  from  the  suii  were  always  the  same ;  that 
is,  if  its  orbit  were  a  circle,  the  earth  would  pass 
through  equal  portions  of  it  in  equal  times.  But  as  the 
earth's  distance  from  the  sun  is  constantly  changing  ; 
that  is,  its  orbit  is  an  ellipse,  the  earth  must  pass  through 
unequal  portions  of  its  orbit  in  equal,  times.  That  is, 
it  passes  through  greater  portions  in  some  days  than  in 
others. 

118.  To  illustrate  this,  (PI.  VI,  fig.  1,)  let  the  plane 
of  the  earth's  orbit  be  divided  into  12  equal  areas,  by 
drawing  lines  from  the  sun  to  1,2,  3,  4,  &c.  In  order 
that  a  line  drawn  from  the  sun  to  the  earth  may  pass 
over  equal  areas  in  equal  times,  the  earth  must  pass  in 
her  orbit  from  one  of  these  lines,  1,2,  3,  4,  &c.  tc 
another  in  equal  times,  that  is,  in  a  month,  reckoning 
12  months  to  a  year.  But  it  is  manifest  that  the  por- 
tions of  the  orbit  between  these  lines  are  unequal.  For 
example,  the  distance  from  1  to  2  is  greater  than  from 
6  to  7.  Hence  the  earth  must  pass  through  a  greater 
portion  of  its  orbit  in  one  month  than  in  another ;  and 
consequently,  through  more  in  some  days  than  in  others. 

119.  It  was  stated,  (No.  105,)  than  in  a  natural  or 
solar  day,  the  earth  turned  a  little  more  than  once  on 
its  axis  ;  and  this  takes  place  became  the  earth  has  ad- 
vanced in  its  orbit.     Hence  as  the  earth  advances  in  its 


Equation  of  Time,  65 

orbit  farther  in  one  day  than  in  another,  the  earth  must 
turn  on  its  axis  farther  in  one  day  than  in  another ;  that 
is,  some  days  are  longer  than  others.  (PL  V,  fig.  2,)  if 
tlie  earth  in  one  part  of  its  orbit  move  from  A  to  B  in 
a  day,  the  excess  over  a  complete  rotation  on  its  axis, 
in  the  same  time,  is  e  o.  But  if  the  earth  in  another 
part  of  its  orbit  should  move  through  a  distance  equal 
to  A  C,  the  excess  here  would  be  e  o,  greater  than  e  o 
in  the  other  case.  So  far  as  this  cause  operates,  the 
sun  vv  ill  agree  with  the  clock  only  at  the  earth's  peri- 
helion and  aphelion ;  that  is,  a  little  after  the  times  of 
the  solstices. 

120.  The  second  cause  of  the  inequality  of  natural 
days,  i^  the  ohliquity  of  the  ecliptic.  If  the  sun  moved 
uniformly  in  the  celestial  equator,  it  is  plain  that  equal 
portions  of  the  earth's  equator  and  all  parallels  of  lati- 
tude would  pass  under  the  suh's  meridian  in  equal 
times;  that  is,  15^  every  hour.  Eut  the  sun's  apparent 
motion  is  not  in  the  celestial  equator,  but  in  the  eclip- 
tic ;  and  equal  portions  of  the  ecliptic  do  not  corre- 
spond with  similar  portions  of  the  celestial  equator. 
Consequently,  the  sun  appears  sometimes  farther  east- 
ward, sometimes  farther  westward,  than  it  would,  were 
it  in  the  celestial  equator ;  and  the  earth  must  turn  on 
its  axis  farther  on  some  days  than  on  others,  to  bring 
the  same  place  under  the  sun's  meridian. 

121.  To  illustrate  this,  (PI.  VI,  fig.  2,)  let  <Y>  JV:f:^:  S 
be  the  concave  heavens,  in  the  centre  of  which  is  the 
earth.  Let  the  line  ^  £hhe  the  celestial  equator,  and 
^  ab  ^^  &c.  be  the  ecliptic.  Let  ^  Ij  1  2,  2  3,  <^c.  be 
equal  distances  on  the  celestial  equator,  and  ^  «,  a  6, 
h  £5,  &c.  be  equal  portions  of  the  ecliptic,  correspond- 
ing to  op  1,  1  2,  &c.  If  a  star  be  supposed  to  start  from 
cf  with  the  sun,  and  move  round  the  earth  in  tuc  celes- 
tial equator,  in  the  same  time  that  the  sun  appears  to  in 
the  ecliptic,  it  is  plain  that  the  star  would  pass  through 

7 


66  Equation  of  Time, 

just  as  many  degrees  in  a  given  time  as  the  sun  would ; 
and  would  arrive  at  the  points  1,  2,  3,  &c.  at  exactly 
the  same  time  that  the  sun  does  at  the  points  a  6,  25  &c. 
When  the  sun  and  star  are  both  together  at  <f ,  they 
are  in  the  same  meridian  ;  hut  when  the  star  comes  to  1, 
and  the  sun  to  a,  they  are  not  in  the  same  meridian,  but 
the  sun  is  westward  of  the  star's  meridian ;  conse- 
quently as  the  earth  turns  on  its  axis  from  west  to  east, 
any  particular  place  will  come  under  the  sun's  meridian 
sooner  than  under  the  star's  meridian ;  that  is,  it  is  noon 
by  the  sun  before  it  is  by  the  star  or  by  a  dock,  (For 
were  the  sun  where  the  star  is,  the  sun  would  agree 
with  the  clock.)  The  case  is  the  same  while  the  sun 
is  between  ^  and  Zd,  and  the  star  between  ^  and  3; 
that  is,  during  one  quarter  of  the  year. 

122.  When  the  sun  comes  to  Z5,  and  the  star  to  3, 
they  are  again  on  the  same  meridian,  and  time  is  the 
same  as  indicated  by  either.  But  while  they  are  mov- 
ing from  23  and  3  to  ^^ ,  the  sun's  meridian  is  to  the 
eastward  of  the  star's  meridian.  Consequently,  places 
on  the  earth's  surface  come  imder  the  sun's  meridian 
later  or  after  they  come  to  that  of  the  star ;  that  is,  it  is 
noon  by  the  sun  later  than  by  the  clock.  At  ^  they 
again  come  into  the  same  meridian.  While  passing 
through  the  remaining  half  of  the  celestial  equator  and 
ecliptic,  precisely  the  same  takes  place  ;  that  is,  it  is 
noon  by  the  sun  sooner  than  by  the  clock  in  the  first 
part,  and  later  in  the  last. 

123.  From  this  cause  of  inequality  in  solar  days,  ii 
is  obvious  that  the  sun  and  clock  would  agree  only  four 
times  in  a  year,  viz.  at  the  equinoxes  and  solstices ; 
also,  that  during  the  first  and  third  quarters,  from  the 
equinoxes  to  the  solstices,  the  sun  would  be  fast  of  the 
clock;  during  the  second  and  fourth  quarters,  from  the 
solstices  to  the  equinoxes,  the  sun  would  be  slow  of  the 
clock. 


Equation  of  Time,  67 

124.  But  the  two  causes  of  which  we  have  spoken, 
counteract  each  other's  effects  in  such  a  manner,  that 
the  sun  and  clock  do  not  agree  at  any  period  when  they 
would  by  the  operation  of  either  cause  singly.  They 
are  together  only  when  the  swiftness  or  slowness  of 
equation,  resulting  from  one  cause,  just  balances  the 
slowness  or  swiftness  arising  from  the  other.  This  is 
the  case  four  times  in  a  year,  viz.  about  the  15th  April, 
15th  June,  31st  August,  and  24th  December.  The 
greatest  possible  difference  between  mean  and  apparent 
time  is  16^  minutes,  which  happens  about  the  first  of 
November,  when  the  sun  is  fast  of  the  clock. 


(  68  ) 


TABLE 


Showing  the  Eqvafion  of  Time,  wtthm  a  minute,  being  cal- 
ailoted  f'rr  the  second  year  after  leap  year. 


M-nths. 
Days 

Equation 

1           in 
Minutes 

Montlis. 

Days. 

Equation 

in 
Minutes. 

Months. 
Days. 

Equation 

in 
Minutes. 

-a 
o 

Days. 
Equation 

in 
Minutes. 

Jan.  1 

4-flApr.  1 

4+ 

Aug.  9 

5+ 

Oct. 

27i  16— 

3 

5 

I     4 

3 

15 

4 

Nov 

15 

15 

5 

t) 

7 

2 

20 

3 

20 

14 

7 

7 

i     11 

I 

24   2 

24 

13 

9 

6 

15 

0 

281   1 

27|  12  1 

12 
15 

9 
10 

* 

31!   U 

* 

on'  n 

19 

l-_ 

Dec 

2 

5 

10 

18 

11 

24 

2 

Sept.  3:   1— 

9 

21 

12 

30 

3 

()!   2- 

7 

8 

25 

13 

May  13 

4 

9   3 

9 

7 

31 

14 

29 

3 

12   4 

11 

6 

Feb.  10 

15 

June  5 

2 

15 

5 

13 

5 

21 

14 

10 

1 

18 

6 

16 

4 

27 

13 

15 

0 

21 

7 

18 

3 

Mar.   4 

8 

12 

v, 

24 

27 

8 
9 

20 

o 

11 

20 

1+ 

22   1 

12 

10 

25 

2^ 

30 

10 

24   0 

15 

9 

29 

3 

Oct.  3 

11 

* 

19 

8 

July  5 

4 

6!  12 

26   1+ 

22 

7 

11 

5 

lOl  13 

28   2 

25 

C 

28 

6 

141  14 

30   3 

28 

5 

19i  15 

1 

Those  columns  that  are  marked  -|-,  show  that  the  clock  or  watch 
is  faster  than  the  sun  ;  and  those  marked  — ,  that  it  is  slower 


Of  the  Harvest  Moon.  39 

Art.  4.     Of  tlie  Harvest  Moon. 

125.  If  the  moon  revolved  round  the  earth  in  24 
days,  it  is  manifest  that  its  mean  daily  motion  would  be 
(360-f-24)  15°,  corresponding  exactly  to  one  hour  of 
time,  consequently  the  mean  daily  difference  in  the 
time  of  the  moon's  rising  would  be  one  hour.  But  the 
moon  is  29  J  days  in  passing  from  change  to  change ; 
consequently  her  mean  daily  motion  is  (360~29J) 
12°  12^  12^^,  and  of  course  the  mean  difference  i^  the 
times  of  her  rising  is^  something  less  than  an  hour*  It 
is  about  19  minutes.  "But  it  was  noticed  by  the  hus- 
bandman long  before  astronomers  could  account  for  it, 
that  for  6  or  8  nights,  near  the  full  moons  of  September 
and  October,  the  moon  rose  nearly  when  the  sun  set, 
and  afforded  convenient  light  to  continue  his  occupation. 
From  the  peculiar  advantages  derived  from  these  full 
moons,  the  first  was  called  the  harvest  moon,  the  se- 
cond the  hunter^s  moon. 

126,  In  illustrating  these  phenomena,  for  the  present 
let  us  suppose  the  moon's  orbit  to  lie  in  the  plane  of 
the  ecliptic.  Let  PI.  VI,  fig.  3,  represent  a  common 
globe  rectified  for  Boston;  that  is,  having  Boston  ex- 
actly at  the  top,  and  the  circle  on  which  is  the  word 
EAST,  in  the  horizon.  By  turning  the  globe  on  its  axis 
JVS,  the  eqitafor  is  always  at  the  same  angle  with  the 
horizon,  and  equal  portions  of  it  come  above  the  hori- 
zon in  the  east  in  equal  times.  But  not  so  of  the  ecliptic. 
For  when  the  point  ,Rries  is  in  the  horizon  in  the  east, 
the  preceding  sign  Pisces  lies  very  obliquely  to  the  ho- 
rizon,^  and  forms  but  a  small  angle  with  it.  But  when 
the  point  Libra  is  in  the  horizon  in  the  east,  the  preced- 
ing sign  Virgo  is  nearly  perpendicular  to  the  horizon.^ 
From  these  different  angles  formed  with  the  norizon  by 
different  parts  of  the  ecliptic,  it  is  manifest,  that  a  greater 
portion  of  the  ecliptic  comes  above  the  horizon  m  ?> 


70  Of  the  Hnrvcsi  Moon, 

given  time  (as  I  hour)  when  Aries  is  in  the  east,  than 
when  UI)ra  is  in  the  east.  Suppose  while  the  moon  is 
moving  in  Pisces  ne'dv  Aries,  it  passes  from  1  to  2,  from 
2  to  3,  &c.  daily.  Suppose  while  moving  near  Lihra^ 
it  passes  from  a  to  J,  from  h  to  c,  &c.  daily.  By  turn- 
ing the  globe,  the  points  1,2,  3,  &c.  come  above  the 
horizon  very  nearly  at  once  ;  whereas  the  points  a  b,  c, 
&c.  come  above  the  horizon  in  succession  at  consider- 
able intervals.  Hence  when  the  moon  is  on  successive 
days  in  the  points  1,  2,  3,  &c.  the  difference  in  the 
times  of  her  rising  is  very  small ;  but  w^hile  successively 
in  the  points  a.  b,  c.  &c.  the  difference  in  the  times  of 
rising  is  very  great. 

This'siibject  may  bo  illustrated  much  more  clearly  by  a  globe  than 
by  any  representation  on  paper.  By  pasting  small  black  patches  on 
the  points  1,  2,  3,  &c.  and  on  a,  b.  c,  &c.  at  the  distance  of  12*^  12' 
from  each  other,  and  by  then  turning  the  globe,  a  clear  illustration 
will  be  effected. 

127.  Although  the  differences  in  the  time  of  the 
moon's  rising  are  always  great  when  she  is  in  or  near 
Libra,  and  always  small  when  in  or  near  Aries,  that 
is  in  every  moon,  yet  we  do  not  notice  those  variations 
except  in  autumn.  (In  fact  we  seldom  notice  the 
moon's  rising  at  all  unless  it  be  when  she  rises  near  sun- 
set, or  in  the  evening.)  The  reason  is  that  the  moon 
can  be  full  in  or  near  Aries,  where  the  difference  in  the 
times  of  her  rising  is  leas,t,  only  when  the  sun  is  in  or 
near  Libra ;  that  is,  at  or  near  the  time  of  tne  autum- 
nal equinox. 

128.  It  is  plain  from  the  figure,  tha*  as  latitude  m- 
creases  northward,  the  difference  in  tlic  times  of  the 
moon's  rising  in  or  near  Aries,  decreases.  For  the  part 
of  the  ecliptic,  Pisces,  &c.  makes  a  less  angle  with  the 
horizon.  Beyond  the  polar  circle,  the  moon  is  above 
the  horizon  during  half  its  revolution,  as  the  sun  is  dur- 
ing half  the  year.     And  here  is  obviously  a  wonderful 


Of  iii£  Harvest  Moon.  71 

accommodation  to  the  wants  of  the  inhabitants.  For 
when  the  sun  is  above  the  horizon,  the  moon,  being  in 
the  opposite  part  of  the  echptic,  fulls  below  the  horizon. 
And  when  the  sun  is  below  the  horizon,  and  the  moon's 
light  most  needed,  the  moon  fulls  above  the  horizon ; 
and  at  the  winter  solstice,  the  moon  is  visible  during 
her  second  and  third  quarters  when  her  light  is  greatest, 
and  is  below  the  horizon  only  when  she  reflects  but 
little  light. 

129.  All  these  appearances  take  place  in  south  lati- 
tude as  well  as  in  north,  only  at  a  different  season.  The 
difference  in  the  times  of  the  moon's  rising  is  there 
least  when  the  moon  is  in  or  near  Libra  ;  hence  their 
harvest  moon  comes  when  the  sun  is  in  or  near  Aries^ 
that  is,  in  our  spring.  But  our  spring  is  their  autumn  ; 
so  that  they  derive  the  same  advantages  from  them,  and 
in  the  same  season,  that  we  do. 

130.  The  effects,  as  we  have  stated,  take  place  on 
the  supposition  that  the  moon's  orbit  lies  in  the  ecliptic. 
But  it  does  not,  but  varies  from  it  5^  20\  This  varia- 
tion sometimes  augments  and  sometimes  diminishes  the 
effects,  of  which  we  have  spoken.  When  the  moon's 
ascending  node  is  in  or  near  Aries ^  the  effects  are  in- 
creased, and  the  harvest  moons  are  most  beneficial ; 
but  (when  the  moon's  descending  node  is  in  or  near 
Aries'^  the  effects  are  diminished  and  the  harvest  moons 
are  least  beneficial. 


72  Phenomena  arising  from  the  Atmosphere. 

The  follomng  Table  shows  in  what  years  the  harvest 
vioons  are  most  or  least  beneficial,  from  the  year  1817  to 
1861.  3%e  columns  of  years  under  M  are  those  in  which 
the  harvest  moon  is  most  beneficial ;  those  under  L  are  the 
years  when  it  is  least  beneficial. 


M 

L 

M 

L 

M 

1817 

1826 

1835 

1844 

1853 

1818 

1827 

1836 

1845 

1854 

1819 

1828 

1837 

1846 

1855 

1820 

1829 

1838 

1847 

1856 

1821 

1830 

1839 

1848 

1857 

1822 

1831 

1840 

1849 

1858 

1823 

1832 

1841 

1850 

1859 

1824 

1833 

1842 

1851 

1860 

1825 

1834 

1843 

1852 

1861 

Sect. IV. 


Of  Phenomena  arising  from  the  Earth's  Atmosphere. 

131.  It  is  found  by  experiment,  that^when  a  ray  of 
light  passes  obliquely  from  one  medium  mto  another  of 
different  density,  as  from  air  into  water,  or  from  water 
mto  air,  it  is  bent  out  of  a  straight  course,  and  it  is  said 
to  be  refracted.  For  example,  (PL  VI.  fig.  4,)  if  a  ray 
from  the  sun  through  the  air  fall  obliquely  upon  water, 
or  any  transparent  fluid,  at  F,  instead  of  continuing  in 
that  direction  to  o,  it  will  be  bent  downwards  to  Q;  so 
that  if  a  diver  should  place  his  eye  at  Q,  he  would  see 
the  sun  at  s  instead  of  S.  The  degree  of  refraction, 
that  is,  the  distance  between  s  and  S,  is  greater  as  the  fluid 
is  more  dense  ;  and  also  as  tlie  ray  falls  upon  it  more  ob^ 
liquely. 


Phenomena  arising  from  the  Atmosphere.  73 

132,  A  very  familiar  experiment  will  illustrate  this 
subject.  Put  a  small  piece  of  money  in  the  bottom  of 
a  bowl,  (PL  VII,  fig.  1  ;)  let  a  person  fix  his  eye  at  .^, 
so  that  he  cannot  see  the  money,  but  a  spot  a  little 
above  it,  as  B.  If  water  be  poured  into  the  bowl  care- 
fully, so  as  not  to  stir  the  coin,  presently  it  will  appear 
to  be  at  J5,  and  become  visible  to  the  eye  at  A.  Had 
the  bowl  a  glass  bottom,  another  person  might  look  up 
through  the  water,  and  see  the  eye  of  the  other  at  a. 
The  reason  of  this  appearance  is  that  the  light  passing 
from  the  money  through  the  water  into  the  air,  is  re- 
fracted just  as  much,  as  when  passing  from  the  air  into 
the  water,  only  in  a  different  direction. 

133.  From  what  has  been  stated,  it  is  manifest  that 
if  a  ray  of  light  pass  through  several  media,  as  A,  B,  C, 
D,  (PL  VII,  fig.  2,)  of  different  densities,  increasing 
downward,  it  will  be  refracted  more  and  more,  as  it 
passes  from  one  medium  into  another;  like  the  lines 
aby  be  J  cd,  de.  Also  ifjlBCD  be  one  medium,  uniform- 
ly increasing  in  density  downward,  a  ray  of  light,  in- 
stead of  describing  the  lines  ab,  be,  &c.  would  proceed 
in  a  curve  line  like  fg. 

]  34.  Now  the  earth's  atmosphere  is  such  a  medium, 
(its  density  is  greatest  at  the  surface  of  the  earth,  and 
decreases  uniformly  upward,  till  the  atmosphere  to 
appearance  vanishes  at  the  height  of  about  45  miles. 
Hence  all  rays  of  light,  which  enter  the  atmosphere 
obliquely,  come  to  us  in  curve  lines.  But  we  always 
see  objects  in  the  direction  in  which  the  light  meets  the 
eye.  Hence  an  obvious  effect  of  refraction  by  the 
earth's  atmosphere  is,  that  we  never  see  any  heavenly 
body  in  its  true  place,  unless  it  be  in  the  zenith,  where 
its  rays  do  not  fall  obliquely  on  the  atmosphere.  The 
sun,  moon,  and  planets  can  never  be  in  the  zenith  of 
Boston  'y  hence  we  can  never  see  any  of  them  where 
they  actually  are. 


74  Phenomena  arising  from  the  Atmosphere. 

1S5.  Refraction  makes  a  heavenly  body  appear  to  be 
higher  above  the  horizon,  than  it  really  is.  To  illustrate 
this  (PL  VII,  fig.  3)  let  H  o  be  the  sensible  horizon  to 
a  person  at  l).  When  a  star  is  at  a,  it  will,  on  account 
of  refraction,  appear,  to  a  person  at  D,  at  h.  So  when 
the  sun  is  actually  below  the  horizon,  at  T,  and  conse- 
quently not  risen,  it  appears  above  the  horizon  at  S, 
In  like  manner  when  it  sets.  Hence  we  see  the  sun 
and  moon  longer  than  they  are  really  above  the  horizon. 
From  this  cause  arose  the  singular  phenomenon  re- 
Corded  in  history,  that  the  moon  totally  eclipsed  was 
visible  in  the  east  while  the  sun  was  visible  above  the 
horizon  in  the  west.  It  has  been  ascertained  that  the 
sun  is  visible  on  account  of  refraction  about  3  minutes 
before  he  rises,  and  about  the  same  time  after  he  sets 
on  a  medium  through  the  year.  Six  minutes  are  thus 
added  to  the  length  of  the  day ;  making  in  the  course 
of  a  year  about  a  day  and  a  half.  This  effect  is  in- 
creased towards  the  poles. 

136.  But  we  have  light  less  or  more  faint,' some  time 
before  and  after  the  sun  is  visible.  This  is  caused 
partly  by  refraction,  but  principally  by  reflection,  of  the 
sun's  i-ays  by  the  atmosphere.  This  foint  light  before 
sunrise  and  after  sunset,  is  called  twilight.  It  com- 
mences in  the  morning  and  ends  in  the  evening,  when 
the  sun  is  18*^  below  the  horizon.  But  the  sun's  ap- 
parent daily  course  is  more  oblique  to  the  horizon  at 
some  places  than  at  others ;  and  at  one  season  of  the 
year,  more  than  at  another,  at  the  same  place.  Hence 
there  is  great  difference  in  the  times  occupied  by  the 
sun  in  passing  through  these  18^.  As  the  latitude  is 
greater,  his  course  is  more  oblique  to  the  horizon,  and 
the  twilight  is  longer.  For  example,  twilight  is  longer 
at  Boston  than  at  New  Orleans,  and  shorter  than  at 
London.  Twilight  is  also  longer  in  summer  than  in 
winter.     At  Boston  the  longest  twilight  is  about  the 


Phenomena  arising  from  the  Atmosphere,  75 

lime  of  the  summer  ^glstice,  and  the  shortest  near  the 
1st  of  March  and  October;  but  uniformly  shorter  in 
winter  than  in  summer.  The  first  appearance  of  morn- 
ing twihght  is  usually  called  davm  or  day  break, 

137.  The  evening  twilight  is  longer  than  the  morn- 
ing ;  principally  because  the  heat  of  the  sun,  during  the 
day,  raises  clouds  and  vapours,  which  increase  the 
density  of  the  atmosphere.  Were  there  no  atmosphere 
to  reflect  ^nd  refract  the  sun's  rays,  the  sky  would  ap- 
pear black,  except  where  the  sun  is  ;  at  sun-set  we 
should  pass  at  once  from  full  day  light  to  darkness, 
(save  the  little  light  which  the  moon  and  stars  afford,) 
and  vice  versa  Qt  sunrise. 

138.  There  are  many  curious  appearances  resulting 
from  refraction.  From  what  has  been  stated,  it  follows 
that  ref|action  is  greatest/when  the  luminary  is  in  the 
horizon,)  and  gradually  diminishes  toward,  the  zenith, 
where  it  entirely  ceases.  When  the  sun  or  moon  is  in 
the  horizon,  as  the  upper  side  is  higher  or  nearer  the 
zenith  than  the  lower,  rays  coming  from  the  upper  side 
are  less  refracted  than  those  coming  from  the  lower. 
Hence  the  difference  between  the  true  and  apparent 
place  of  the  lower  edge  of  the  sun  or  moon  is  greater 
than  of  the  upper  edge  ;  consequently  the  figure  of 
these  luminaries  in  the  horizon  is  often  observed  to  be 
oval  or  elliptical,  instead  of  circular. 

139.  When  the  moon  is  totally  eclipsed  she  is  seldom 
invisible,  but  appears  of  a  colour  somewhat  resembling 
that  of  tarnished  copper.  Now  since  the  moon  is  at 
such  times  wholly  in  the  earth's  shadow,  how  is  it  that 
she  is  at  all  visible  ?  It  is  generally  supposed,  and  it 
can  scarcely  be  doubted,  that  this  effect  is  produced  by 
the  refractive  power  of  the  earth's  atmosphere.  The 
sun's  rays,  passing  through  our  atmosphere,  are  bent 
inwards ;  so  that  the  earth's  shadow  at  the  distance  of 
the  moon  is  not  gross  darkness.     A  few  refracted  rays 


76  Phenomena  arising  from  the  Atmosphere, 

fall  upon  the  moon,  and  being  reflected  back  render 
her  visible  to  us. 

140.  Refraction  makes  not  only  heavenly  bodies,  but 
also  objects  on  earth  appear  higher  than  they  really 
are.  For  example,  when  we  look  at  objects  actually 
higher  than  we  are,  as  a  mountain  or  steeple,  they  ap- 
pear still  higher  than  they  actually  are.  For  the  atmo- 
sphere being  more  dense  near  the  earth's  surface,  where 
we  are,  and  rarer  upwards,  where  the  objects  are  to 
which  we  look,  the  light  coming  from  those  objects 
passes  in  curve  lines,  bei.ding  downwards.  This  effect  is 
not  great  when  the  objects  are  nigh.  But  if  they  are 
at  considerable  distance,  it  may  amount  to  several  feet. 
The  most  striking  effect  of  this  kind  is  witnessed  at  sea. 
Jn  thick  foggy  weather,  a  vessel  at  considerable  distance 
is  often  so  elevated  and  magnified,  (or  looms  up,  as  sea- 
men call  it,)  that  it  appears  to  be  very  near. 

Atmospherical  appearances  have  always  been  resorted  to  as  indi- 
cations of > the  coming  weather,  with  more  or  less  success,  according 
to  the  variableness  of  the  climate,  and  the  acuteness  and  experience 
of  observers.  General  principles  there  undoubtedly  are,  by  which 
prognostics  may  often  be  made  witli  a  great  degree  o^  certainty. 
Baroi.  Humboldt  remarks  that '' under  the  torrid  zone,  where  the 
meteorological  phenomena  follow  each  other  with  great  regularity,  and 
where  the  horizontal  refractions  are  more  uniform,  the  prognostics 
are  surer  than  in  the  northern  regions.  A  great  paleness  of  the  set- 
ting sun,  a  wan  colour,  an  extraordinary  disfiguration  of  its  disk  are 
almost  unequivocal  signs  of  a  tempest ;  and  we  can  scarcely  conceive, 
how  the  state  of  the  low  strata  of  the  atmosphere  (indicated  by  these 
appearances),  can  be  so  intimately  connected  with  meteorological 
changes,  that  take  place  eight  or  ten  hours  after  the  setting  of  the 
sun. 

''  Mariners  have  carried  the  physiognomical  Knowledge  of  the 
sky  to  a  n^iuch  higher  state  of  perfection,  than  the  inhabitants  of 
the  fields.  Viewing  only  the  ocean,  and  the  sky  which  seems  to 
repose  upon  its  surface,  their  attention  is  continually  fixed  on  the 
slightest  modifications  of  the  atmosphere.  Among  the  great  num- 
ber of  meteorological  rules,  which  pilots  transmit  to  each  other  as 
a  kind  of  inheritance,  there  are  several  that  evince  great  sagacity  ; 
and  in  general,  prognostics  are  less  uncertain  in  the  basin  of  the 
6easj  especially  in  the  equinoctial  parts  of  the  ocean,  than  on  the 


Phenomena  arising  from  the  Atmosphere.  77 

continent,  where  the  configuration  of  the  ground,  mountains,  and 
plains,  interrupts  the  regularity  of  the  meteorological  phenonr.ena. 
The  influence  of  the  lunations  on  the  duration  of  tempests;  the 
action  exercised  by  the  moon  at  its  rising,  during  several  successive 
dajT^s,  on  the  dissolution  of  the  clouds ;  the  intimate  connexion  that 
exists  between  the  descent  of  marine  barometers  and  the  changes 
of  weather ;  and  other  similar  facts;  are  scarcely  observed,  in  in- 
land countries  comprised  in  the  variable  zone,  while  their  reality 
cannot  be  denied  by  those,  who  have  long  been  in  the  habit  of 
sailing  between  the  tropics." 


141.  Though  it  properly  belongs  to  the  science  of 
optics  and  not  to  astronomy,  yet  it  may  not  be  uninter- 
esting to  explain  here  what  is  called  the  horizontal 
moon.  Every  one  must  have  observed  that  the  sun 
and  moon  appear  bigger  in  the  horizon,  than  when  con- 
siderably above  it  near  the  zenith.  This  appearance  is 
supposed  to  result  entirely  from  error  in  our  judgment. 
We  insensibly  consider  the  horizon  at  a  greater  distance 
from  us  than  the  zenith.  Hence  the  sky  above  tlie 
horizon  does  not  appear  to  us  to  form  a  concare  hemi- 
sphere, but  a  figure  somewhat  like  the  crystal  of  a 
watch.N 

142.  To  show  how  this  circumstance  accounts  for 
the  phenomenon  under  consideration,  we  must  st'dte, 
thatU/i  judging  of  the  unknown  size  of  any  object^  we 
always  first  judge  of  the  distance  of  that  object.  For 
example,  in  looking  at  a  calf,  if  I  can  see  all  the  inter- 
vening objects,  and  rightly  estimate  its  distance  to  be 
100  rods,  I  shall  probably  judge  rightly  of  its  size,  and 
not  mist9.ke  it  for  an  ox.  But  if,  by  any  impediments, 
I  should  judge  wrongly  of  its  distance,  and  consider  it 
500  rods  instead  of  100,  I  should  undoubtedly  judge 
wrongly  of  its  size,  and  might  mistake  it  for  an  ox. 
Universally  if  two  objects  of  equal  size,  and  at  equal 
distances  from  us,  be  judged  to  be  at  unequal  distances 
from  us,  the  one  which  we  consider  most  dis^tant  we 
shall  consider*  lartjest. 


78 


Phenomena  arising  from  the  Atmosphere. 


143.  Now  when  the  moon  is  in  the  horizon,  we  see 
intervening  objects  ;  but  when  above  the  horizon,  we  do 
not.  Suppose  I  observe  the  moon  to  rise  apparently  by 
the  side  of  the  trunk  of  a  tree,  which  I  well  know  to  be 
200  or  300  rods  distant ;  and  which  I  also  well  know  is 
nearly  2  feet  in  diameter,  where  it  appears  in  the  hori- 
zon. I  see  the  moon  is  beyond  that  tree,  and  that  its 
apparent  diameter  is  greater  than  that  of  the  tree  ;  I 
hence  insensibly  estimate  the  diameter  of  the  moon  to 
exceed  2  feet ;  whereas  in  the  zenith  I  think  it  scarce 
six  inches.  It  is  from  the  same  cause  that  in  looking 
across  water,  or  an  extensive  marsh,  we  always  think 
the  distance  less  than  it  really  is  ;  there  being  few  in 
termediate  objects. 

These  estimates  are  made  for  illustration  only.     Different  peop'^ 
form  very  different  estimates  of  the  apparent  diameter  of  the  sun  ap^ 


To  render  this  subject  more 
plain,  the  annexed  figure  is 
introduced.  Let  us  suppose 
an  observer  at  JB,  while  the 
moon  passes  from  the  hori- 
zon at  A  through  B  and  C 
to  the  zenith  D.  If  the  ob- 
server considers  the  moon  as 
passing  through  a  part  of  a 
circle,  and  always  at  the  same 
distance  at  B,  C,  and  D,  the 
moon  will  appear  to  him  al- 
ways of  the  same  size.  But 
if,  while  the  moon  passes  from 
A  through  the  stations  B,  C, 
and  D,  it  appears  to  him  that 
it  passes  from  A  through  the 
stations  b,  c,  and  d,  it  will  appear  to  him  less  at  6,  than  at  Aj  and  less 
at  c  and  d  than  at  h.  Now  this  last  is  the  true  appearance  of  the 
moon,  while  she  rises  from  the  horizon  A  to  the  zenith  D  in  the  cir- 
cle ABCD,  she  appears  to  us  to  move  in  the  depressed  curve  A  h  c  dy 
thus  continually  becoming  nearer  Thus  we  attribute  to  her  a  vari- 
ation in  size,  because  there  appears  to  be  a  variation  in  her  divStance 


Phenomena  arising  from  Magnityde.  79 


Sect.  V. 

Of  Phenomena  arising  from  the  Earth\s  Mcgnitude. 
PARALLAX. 

144.  None  of  the  heavenly  bodies,  unless  they  be 
in  the  zenith,  appear  to  have  the  same  place  among  the 
stars  when  seen  from  the  earth's  surfcce,  that  they  would 
have,  if  seen  from  the  earth's  centre.  To  a  spectatoi 
at  G,  (PI.  VII,  fig.  4,)  the  centre  of  the  earth,  the  moon 
at  jE  would  appear  among  the  stars  at  /;  but  seen  from 
the  surface  of  the  earth  at  .3,  it  would  appear  at  K.  The 
place  /  is  its  true  place,  and  K  its  apparent  place  ;  and 
the  difference  between  them  is  its  parallax^  diurnal 
parallax^  or  horizontal  parallax.  As  the  moon  comes 
above  the  horizon,  say  to  i),  its  parallax  decreases ;  for 
here  it  is  H  a,  less  than  Ilv,  And  when  the  moon 
comes  to  the  zenith  at  F^  parallax  ceases ;  for  it  ap- 
pears at  Z^  w  licther  seen  from  G  or  A. 

145.  {The  parallax  of  a  heavenly  body  is  less  as  its 
distance  is  greater.  If  the  moon  were  at  e  instead  of  E, 
its  parallax  would  be  n  K  instead  c  f  IK,  The  moon's 
horizontal  parallax  is  about  57' ;  the  sun's  8'^  The 
distance  of  the  stars  is  so  great,  that  no  parallax  can  be 
discovered. 

146.  Refraction  and  parallax  both  make  bodies  ap- 
pear  where  they  are  not ;  but  refraction  elevates  them^ 
and  parallax  depresses  them.  They  are  both  greatest 
in  the  horizon,  and  vanish  at  the  zenith.  The  moon  is 
depressed  by  parallax  near  twice  as  much  as  it  is  ele- 
vated by  refraction  ;  but  the  sun  is  depressed  by  paral- 
lax only  about  ^^o  as  much  as  it  is  elevated  by  refrac- 
tion. Refraction  is  the  same,  whether  the  light  come 
from  the  sun,  moon,  or  any  other  heavenly  body ;  be- 
ing generally  about  33'  in  the  horizon. 


8D  FJieno-rmv^i  an^v]g  fi-^m  Magmtiide. 

14  7.  Parallax  or  diurniil  piralax  is  to  be  understood 
as  abc'/e  explained.  But  there  is  an  annual  parallax; 
by  waieh  is  meant,  ihg  diffeTgnce  In  the  apparent  place 
of  a  hi:avenly  boi/,  g.s  ssea  iom  the  earth  in  opposite 
points  of  its  orbit.  As  the  mean  distance  of  the  earth 
from  tlie  sun  is  93  millions  of  miles,  it  is  obvious  that 
the  eaj'th,  in  one  part  of  its  orbit,  as  at  Zd,  is  (2x^3) 
186  Tin:ilions  of  miles  farther  eastward,  than  when  in  the 
opposite  part,  as  at  VJ.  Hence  we  might  suppose,  that 
if  a  particular  star  is  exactly  in  the  north  when  the  earth 
is  in  one  part  of  its  orbit,  it  would  deviate  somewhat 
from  the  north,  when  the  earth  comes  to  the  opposite 
point.  (For  the  earth's  axis  is  ahvays  parallel  with  it- 
self) But  the  pole  star  (and  indeed  all  stars)  have  no 
annual  parallax,  that  can  be  discovered  ;  owing  to  their 
inconceivable  distance.  The  nicest  instruments,  which 
the  m«  St  ingenious  artists  have  been  able  to  construct, 
fail  entirely  to  indicate  to  us  any  deviation  arising  from 
this  cause  of  any  star  from  its  true  place.  But  these 
instruments  would  indicate  such  deviation,  were  not  the 
stars  more  ^han  200,000  times  farther  off  than  we  are 
from  the  sun.  (18,600,000  millions  of  miles>)  The 
probability,  is,  tha  1  the  nearest  stars  are  at  a  much 
greater  distance. 


The  following  A^umbers  of  this  section  cannot  be  fully 
understood  urithout  a  knowledge  of  plane  Trigonometry. 
They  may  therefore  be  omitted  by  those  who  are  ignorant 
of  that  branch  of  mathematics, 

148.  The  distance  of  the  moon  was  long  since  ascer- 
tained with  the  utmost  accuracy  by  means  of  her  paral- 
lax. There  are  several  methods  of  obtaining  this  paral- 
laX;  ami  of  applying  it.  The  following  is  one  of  the  most 
sure  and  simple.  Let  us  suppose  that  two  observers 
ar^  at  the  points  A  and  B  in  the  same  meridian ;  and 
l'^    the  distance  between  them,  that  is,  their  diflerence 


Phenomena  aris-ing  from  Magniitide, 


61 


of  latitude,  be  previously 
known.  When  the  moon 
M  passes  the  meridian  of 
these  observers,  let  each, 
with  a  good  instrument,  take 
her  zenith  distance ;  that  is, 
the  arc  ZM  and  zM.  In 
the  triangle  AOB,  the  sides 
OA  and  OB  are  each  equal 
to  the  semidiameter  of  the 
earth,  which  is  known ;  and 
the  angle  AOB  is  measured 
by  the  arc  AB^  which  is  the 
difference  of  latitude  be- 
tween the  observers,  and  is 
also  known  (by  the  supposition.)  These  three  thmgs 
therefore  being  known,  we  can  readily  calculate  the 
length  of  the  side  AB,  and  the  magnitude  of  the  angles 
OAB  and  OBA, 

149.  Now  the  zenith  distances  ZM  and  zJ\'L  (which 
have  been  observed)  measure  the  angles  ZAM  and 
zBM.  If  then  each  of  these  angles  be  taken  from  1 SO^, 
we  have  the  angles  0AM  and  OBM.  If  from  the 
angle  0AM  we  take  the  angle  OAB,  we  get  the  angle 
MAB ;  and  if  from  the  angle  OBM,  we  take  the  an- 
gle OBA,  we  get  the  angle  MBA.  Here  then  in  the 
triangle  MAB,  the  angles  MAB  and  MBA,  and  the 
side  AB  are  known  ;  and  hence  can  be  found  the  side 
MB,  which  is  sufficient  for  our  purpose.  Now  in  the 
triangle  MBO,  these  three  things  are  known,  viz.  the 
sides  MB  and  BO,  and  the  included  angle  MBO  ; 
hence  may  be  found  the  length  of  the  side  MO,  which 
is  the  distance  of  the  moon  from  the  earth.  In  the 
same  way  might  the  distance  of  other  heavenly  bodies  be 
found,  were  not  their  distance  so  great  and  the  parallax 
so  small  that  accurate  observations  could  not  be  made. 

Proper  allowance  must  here  V/e  made  for  refraction. 


82  Phenomena  ansing  from,  Magnitude, 

150.  The  ancients,  so  far  as  we  know,  were  quite 
ignorant  of  the  real  distance  of  the  earth  from  the  sun. 
The  solution  of  this  problem  baffled  the  skill  and  mock- 
ed the  toil  and  industry  of  astronomers  for  ages ;  and  it 
was  not  till  very  lately  that  any  certain  knowledge  wa« 
gained  on  this  subject.  The  first  approximation  to- 
wards the  truth  was  obtained  by  observing  as  correctly 
as  possible  the  precise  time  when  half  the  moon's  visi- 
ble hemisphere  is  enlightened.  For  it  will  be  obvious 
on  a  little  reflection,  that  this  must  be  the  case  when 
the  plane  of  the  circle  dividing  her  dark  from  her  illu- 
minated hemisphere,  would  pass  through  the  centre  of 
the  earth  ;  and  this  takes  place  a  little  before  the  first 
quarter  and  a  little  after  the  third  quarter.  When  this 
is  the  case,  the  angle  made  at  the  moon  by  lines  drawn 
to  the  sun  and  to  the  earth,  is  a  right  angle.  By  ob- 
servino^  the  number  of  deorees  between  the  moon  and 
sun  at  this  time,  the  angle  made  at  the  earth  by  lines 
drawn  to  the  sun  and  moon  is  obtained.  And  the  dis- 
tance of  the  moon  from  the  earth  is  already  known. 
Here  then  is  a  triangle,  of  which  two  angles  and  one 
side  are  known  ;  and  hence  the  ether  sides  may  be 
obtained,  one  of  which  is  the  distance  of  the  earth  from 
the  sun. 

151.  But  no  observation  can  be  fully  relied  on  for 
determining  the  very  moment  when  half  the  moon's 
visible  hemisphere  is  enlightened  ;  that  is,  vvlien  the 
line,  dividing  the  dark  from  the  light  portion  of  the 
moon's  disk,  is  a  straight  line.  Some  other  means  was 
therefore  to  be  devised  for  ascertaining  accurcitciy  the 
real  distance  of  the  earth  from  the  sun.  Dr.  Halley  in 
1691  devised  the  method  of  finding  this  distance  by 
observing  a  transit,  (that  is,  a  passing,)  of  Venus  over 
the  sun's  disk,  hence  deducing  the  sun's  parallax.  As 
no  transit  occurred  in  his  day,  he  could  only  call  the 
attention  of  future   astronomers  to  these    phenomena. 


Phenomena  arising  from  Magnitude.  83 

when  they  s'hoiild  occur.  A  transit  took  place  in  1761, 
and  another  in  1769 ;  on  both  which  occasions  astrono- 
mers went  into  different  parts  of  the  world  in  order  to 
take  (  .  servations  under  a  variety  of  circumstances.  But 
the  observations  of  the  latter  transit  did  little  more  than 
confirm  the  result  derived  from  the  observation  of  the 
former. 

152.  Before  we  proceed  to  show  how  the  parallax 
of  the  sun  can  be  obtained  from  a  transit  of  Venus,  (t 
may  be  useful  to  state  some  of  the  facts  and  principles 
respecting  the  motions  and  orbits  of  the  planets,  which 
were  actually  discovered  from  observation,  and  most  of 
which  were  necessary  to  be  known  before  the  sun's 
parallax  could  be  found. 

1st.  By  ^observations,  astronomers  had  determined 
the  precise  time  in  which  each  planet  completes  its 
revolution. 

2d.  Kepler,  by  comparing  observations,  developed 
this  law,  viz.  The  squares  of  the  periodical  times  of  the 
planets  are  to  each  other  as  the  cubes  of  their  distances 
from  the  sun.  Hence,  since  the  periodical  times  are 
known,  the  relative  distances  of  the  planets  from  the 
sun  are  readily  found.  For  example,  let  the  periodical 
times  of  Venus  and  the  earth  be  known,  and  let  us  sup- 
pose the  distance  of  the  earth  from  the  sun  to  be  10; 
then  say,  as  the  square  of  the  earth's  periodical  time  is 
to  the  square  of  the  periodical  time  of  Venus,  so  is  the 
cube  of  the  earth's  supposed  distance  (10,)  to  the  cube 
of  the  distance  of  Venus  (7^  nearly.)  In  the  same  way 
the  relative  distance  of  the  other  planets  may  be  obtained. 

3d.  By  observation,  the  relative  angular"^  motion  of 
Venus  and  the  earth  was  found ;  and  consequently  the 

*  It  may  be  necessary  for  the  instructer  to  explain  to  the  piipii 
the  difference  between  angular  motion  and  absolute  motion  ;  that  the 
first  is  estimated  by  degrees,  as  seen  from  the  sun,  and  the  second  by 
miles. 


84 


Phenomena  arishig  from  Magnitude, 


excess  of  the  angular  motion  of  Venus  over  that  of  the 
earth, 

4th.  Observation  had  enabled  astronomers  to  deter-_ 
mine  the  position  of  the  orbits  of  Venus  and  the  earthj^-* 
so  that  the  part  or  limb  of  the  sun  might  be  known,  over 
which  Venus  would   appear  to  pass  at  any  particular 
transit ;  and  also  the  direction  and  duration  of  the  tran- 
sit, as  viewed  from  the  earth's  centre. 

153.  Let  us  then  suppose  the  duration  of  the 
transit  to  be  computed  beforehand,  as  seen  from  the 
centre  of  the  earth.     Let  S  be  the  sun,  BEH  part  of 

the  orbit  of  Venus, 
nnd  O  the  earth  in 
*»,s  orbit.  For  tlie 
greater  advantage, 
let  the  transit  be  ob- 
served from  a  place, 
as  jD,  where  the 
sun  will  be  on  the 
meridian  about  the 
middle  of  the  tran- 
sit. Let  us  suppose 
that  Venus  at  B  is 
seen  at  D  as  enter- 
ing on  the  sun's  disk 
at  A,  If  the  place 
D  were  stationary 
with  regard  to  the 
earth's  centre,  Ve- 
nus must  move  by 
the  excess  of  her 
angular  motion  over 
that  of  the  earth, 
from  B  to  Jl,  before 
it   would  appear  to 


'Phenomena  arising  from  Magnitude,  85 

pass  off  the  sun's  disk  at  C ;  the  time  of  doing  which, 
let  us  suppose  to  be  the  same  as  the  calculated  dura- 
tion of  the  transit  as  seen  from  the  earth's  centre.  But 
during  this  time,  by  the  rotation  of  the  earth  on  its  axis, 
the  place  D  is  carried  eastward  to  P,  w^here  it  is  at  the 
end  of  the  transit ;  so  that  instead  of  coming  to  i?,  Ve- 
nus moves  only  to  E  in  its  orbit  before  it  is  seen  passing 
off  the  sun's  disk  at  C,  and  the  transit  is  ended. 

154.  Hence  it  is  obvious,  that  the  duration  of  the 
transit^  as  computed  for  the  earth's  centre,  is  shortened 
by  the  motion  of  the  place  from  D  to  jP,  hy  the  time  it 
would  take  Venus  to  move  from  E  to  H.  Hence  by 
observing  the  difference  between  the  computed  and 
observed  duration  of  the  transit,  we  have  the  time 
which  Venus  takes  in  passing  from  _E  to  iJ  by  the  ex- 
cess of  her  angular  motion  over  that  of  the  earth  ;  and 
since  this  excess  is  previously  known,  by  turning  this 
difference  of  time  between  the  computed  and  observed 
duration  of  the  transit  into  degrees  and  minutes  of  that 
excess,  we  get  the  number  of  degrees  and  minutes 
between  E  and  H,  that  is,  we  get  the  angle  ECH,  or 
DCF,  Now  the  line  DF  may  be  readily  computed 
from  the  latitude  of  the  place  and  the  observed  duration 
of  the  transit ;  and  may  be  compared  with  the  semi  di- 
ameter of  the  earth.  From  this  comparison  would  be 
seen  at  once  the  angle  at  C,  which  a  semidi- 
ameter  of  the  earth  would  subtend ;  that  is,  the  sun's 
parallax.  Let  this  parallax  be  equal  to  the  angle  I-IL, 
subtended  by  the  semidiameter  of  the  earth  IL.  Here 
then  we  have  a  triangle  jE/2L,  of  which  the  angle  at  A 
is  known,  and  the  angle  at  J  a  right  angle,  and  the  side 
IL,  equal  to  the  earth's  semidiameter,  is  knov/n ; 
whence  may  be  known  the  angle  at  L,  and  the  side  AI^- 
w  hich  is  the  earth's  distance  from  the  sun. 


86  Phenomena  arising  from  Magnitude, 

155.  Having  obtained  the  absolute  distance  of  the 
earth  fi-om  the  sun,  and  the  relative  distances  of  all  the 
planets  being  previously  known,  their  absolute  distan- 
ces may  be  at  once  ascertained.  For,  as  the  relative 
distance  of  the  earth  is  to  its  absolute  distance,  so  is  the 
relative  distance  of  any  planet  to  its  absolute  distance. 

In  what  has  been  said  of  the  method  of  finding  the  parallax  of 
the  earth,  and  thence  the  distances  of  the  planets  from  the  sun, 
none  of  the  difficulties  of  its  execution  appear.  Incredible  pains 
were  taken  by  astronomers  in  making  accurate  calculations,  and 
in  providing  the  means  for  numerous  and  accurate  observations, 
previous  to  the  transits  of  1761  and  17C9.  The  skilful  and  scien- 
tific of  Europe  were  scattered  over  the  habitable  globe,  for  the 
purpose  of  observing  this  phenomenon  under  circumstances  as  va- 
rious as  possible.  Some  went  to  India,  others  to  America ;  some 
to  the  north  of  Europe,  others  to  the  south.  The  truth  was  arrived 
at  by  vast  labour  in  comparing  an  almost  endless  variety  of  obser 
vations,  made  at  different  places ;  correcting  the  probable  error  oJ 
one  observation  by  the  probable  opposite  error  of  another  observa 
tion,  thus  taking  a  mean  of  the  whole.  For  a  more  full  account, 
the  pupil  is  referred  to  Ferguson's  Astronomy.  There  wil  not  be 
another  transit  of  Venus  till  the  year  1874. 


Attraction.  87 

BOOK  n. 
PHYSICAL  ASTRONOMY. 

Attraction, 

156.  There  is  one  property  common  to  every  par- 
ticle of  matter  in  the  universe,  viz.  it  tends  to  every 
other  particle.  However  near,  or  however  remote  from 
each  other,  still  they  all  tend  to  each  other,  in  a  greater 
or  less  degree.  (This  universal  tendency  constitutes 
what  is  called  the  principle  of  universal  gravitation  or 
attraction.  If  a  stone  be  flung  into  the  air,  it  comes  to 
the  ground.  The  tendency,  which  causes  it  to  fall,  is 
gravitation.  It  is  precisely  the  same  as  weight.  When 
a  body  is  said  to  weigh  a  pound,  the  meaning  is,  that  the 

(jtendency  of  that  body  to  the  earth  is  equal  to  the  ten- 
dency of  another  body,  called  a  pound  weight.  The 
unknown  tendency  or  gravity  of  one  body  is  compared 
with  the  known  tendency  or  gravity  of  another ;  and  as 
the  unknown  exceeds  or  falls  short  of  the  known,  it  is 
said  to  weigh  more  or  less  than  a  pound.  So  of  any 
number  of  pounds. 

157.  But  this  tendency  or  gravitation  is  not  uniform. 
It  is  varied  by  one  and  only  one  circumstance,  viz.  dis- 
tance. Two  particles  close  together  are  more  strongly 
attracted  towards  each  other,  than  if  far  apart.  But 
this  attraction  varies  according  to  a  certain  known  law. 
It  decreases  as  the  square  of  the  distance  increases.  For 
example,  if  two  particles  be  two  inches  apart,  the  at- 
traction is  4  times  greater  than  if  four  inches  apart ;  for 
the  square  of  2  is  (2  X  2)  4,  and  the  square  of  4  is 
(4  X  4)  16;  and  16  is  four  times  greater  than  4.  The 
very  fact  that  attraction  or  gravitation  operates  in  this 
manner,  proves  that  it  can  never  entirely  c^ase  :  for 
two  bodies  can  never  be  infinitely  distant. 


88  .  Attraction. 

158.  When  there  is  no  distance  between  two  or  more 
particles,  they  adhere  and  form  a  distinct  body ;  which 
attracts  and  is  attracted,  Hke  a  single  particle.  But  as 
every  particle  in  this  body  attracts  every  particle  out  of 
it,  just  as  much  while  they  adhere  as  if  they  were  sepa- 
rate, it  follows  that  one  body  attracts  all  others  more  or 
less  according  to  the  number  of  particles  it  contains  ; 
that  is,  its  solid  contents.  If  a  stone  be  flung  into  the 
air,  it  falls  to  the  earth,  because  the  solid  contents  of 
th?  earth  exceed  those  of  the  stone.  But  the  earth  also 
is  at  the  same  time  drawn  towards  the  stone,  and  ac- 
tually moves  towards  it.  If  the  solid  contents  of  the 
stone  and  of  the  earth  were  equal,  that  is,  if  these  bo- 
dies were  equally  heavy,  they  would  meet  half  way.  If 
the  solid  contents  of  the  stone  exceeded  those  of  the 
earth,  as  much  as  those  of  the  earth  exceed  those  of 
the  stone,  the  earth  would  fall  to  the  stone,  ju«t  as  the 
stone  does  to  the  earth.  Hence  all  attraction  oj  bodies 
is  mutual;  and  greater  or  less,  according  to  their  solid 
contents.-' 

159. (if  two  unequal  bodies  be  drawn  towards  each 
othe»*  by  mutual  attraction,  the  distances  of  the  points, 
whe^r^  they  would  meet  (called  the  centre  of  gravity) 
from  the  points  whence  they  set  out,  will  be  inversely 
as  their  solid  contents.  For  example,  if  a  body  of  40 
pounds,  and  a  body  of  10  pounds,  move  to  each  other 
in  a  straight  line,  the  body  of  10  pounds  will  move  4 
times  faster  than  that  of  40  pounds ;  so  that  if  the  dis- 
tance be  100  yards,  the  centre  of  gravity  is  80  yards 
from  the  point  where  the  body  of  10  pounds  set  out, 
and  20  yards  from  the  point  where  that  of  40  pounds 
set  out.  Whence  it  follows,  that  if  the  weight  of  each 
body  be  midtiplied  into  its  distance  from  the  centre  of 
gravity,  the  product  is  the  same,  (10x80=800,  and 
40x20=800.)  This  is  universally  true,  and  afibrds 
an  easy  method  of  finding  the  centre  of  gravity  of  two 


Attraction.  89 

bodies.  Say,  as  the  weight  of  both  bodies  is  to  tlie 
whole  distance  betvjeen  them,  so  is  the  weight  of  one  to  the 
distance  of  the  other  from  the  centre  of  gravity, 

160.  But  if  every  particle  and  body  of  matter  attracts 
and  is  attracted  by  all  others,  the  question  is  forced 
upon  us,  why  do  they  not  come  together  and  form  one 
body?  Why  does  not  Uranus  fall  upon  Saturn,  and 
both  together  upon  Jupiter ;  and  since  the  solid  con- 
tents of  the  sun  very  much  exceed  those  of  all  the 
planets  together,  why  do  they  not  all  leave  their  orbits 
and  blend  with  him  into  a  common  mass  ? 

161.  Besides  the  tendency,  which  every  body  has  to 
all  others,  there  is  another  circumstance  attending  ina- 
nimate bodies  no  less  universal,  viz.  inertness.  For  ex- 
ample, a  body  at  rest  tends  to  remain  at  rest,  and  re- 
quires a  force  to  put  it  in  motion.  So  a  body  in  mo- 
tion tends  to  move  in  a  straight  line,  and  requires  a 
force  to  turn  it  out  of  a  straight  line.  And  the  swifter 
the  motion  is,  the  greater  is  the  force  required  to  change 
its  direction.  If  a  ball  be  thrown  swiftly  among  nine- 
pins, it  is  not  easily  turned  out  of  a  straight  course  ;  but 
if  slowly,  a  slight  obstruction  gives  it  a  new^  direction. 

162. /We  have  then  these  two  facts  relating  to  bodies  : 
— 1st,  they  attract  each  other  ;  and  this  attraction  de- 
creases as  the  square  of  the  distance  increases.  If  the 
bodies  be  unequal,  they  attract  according  to  their  solid 
contents,  2d,  Every  body  in  motion  (as  all  bodies  are) 
tends  to  move  in  a  straight  line  ;  and  this  tendency  is 
greater  as  the  motion  is  more  rajjid})  By  the  application 
of  these  principles  we  account  for  the  phenomena 
treated  of  in  the  following  sections. 

It  is  to  be  noticed,  that  no  natural  principle  accounts  for  the  origin 
of  motion.  The  origin  of  motion  and  of  life  is  the  same,  God.  We 
find  ourselves  living  creatures ;  we  find  the  bodies  of  the  solar  sys- 
tem in  motion.  Philosophy  as  readily  accounts  for  one  fact  as  the 
other.  Both  are  beyond  its  reach 
9 


90        Motion  of  Heavenly  Bodies  in  their  Orbits. 


SECTION   1. 

Of  the  Motion  of  Heavenly  Bodies  in  their  Orbits, 

163.  Let  S  be  the  sun,  (PI.  VIII,  fig.  1,)  and  the 
earth  at  A  in  motion  towards  B.  Suppose  this  motion 
such  as  would  carry  it  to  B  in  the  time  that  the  sun's 
attraction  would  carry  it  to  C.  Here  the  earth  has  two 
tendencies,  one  to  move  in  the  straight  line  AB,  and 
the  other  to  go  to  the  sun  in  the  direction  ACS.  Which 
of  these  courses  will  the  earth  take  ?  Obviously  nei- 
ther ;  but  will  go  in  a  middle  direction  and  come  to  J5, 
describing  the  part  of  a  circle  AD.  When  at  D,  the 
earth  tends  to  move  in  a  straight  line  towards  Fj  and 
is  also  attracted  by  the  sun  towards  jE.  Here  again  it 
must  take  a  middle  course  and  come  to  G,  describing 
another  portion  of  a  circle.  In  this  way  the  earth 
would  describe  successively  all  the  parts  of  a  circle  and 
come  again  to  A, 

The  force  which  propels  a  planet  in  its  orbit  is  called  the  projec- 
tile  or  centrifugal  force  ;  that  which  draws  it  to  the  centre,  the  cen- 
tripetal force. 

164.  This  shows  how  a  planet  may  revolve  in  a  cir- 
cidar  orbit,  but  not  in  an  elliptical;  and  the  orbits  of  all 
the  planets  are  ellipses.  If  the  earth  revolved  in  a  circle, 
the  power  of  the  sun's  attraction  w^ould  be  always  the 
same;  for  the  earth's  distance  and  solid  contents  would 
be  always  the  same.  But  since  the  earth's  orbit  is  el- 
liptical, its  distance  from  the  sun  is  continually  varying, 
consequently  the  power  or  force  of  the  sun's  attraction 
is  continually  varying.  In  order  therefore  to  bring  the 
earth  back  to  the  point,  whence  it  is  supposed  to  start, 
its  tendency  to  move  in  a  straight  line  must  also  con- 
tinually vary. 

l^'i.  To  illustrate  this,  suppose  the  earth  at  A  in 


Motion  of  Heavenly  Bodies  in  their  Orbits.  9 1 

motion  towards  B  with  a  velocity,  which  would  carry 
it  to  B  in  the  time  that  the  sun  would  draw  it  to  c. 
It  is  plain  that  instead  of  describing  the  part  of  the 
circle  AD^  it  would  describe  a  part  of  a  different  orbit 
Ad.  Ki  d  it  would  tend  to  move  in  the  line  dj\  and 
the  sun  would  draw  it  towards  e  ;  again  it  would  take  a 
middle  course,  and  come  to  g.  In  this  way  it  would 
proceed  onward  to  the  completion  of  half  its  orbit  at  q  ; 
and  this  orbit  is  elliptical. 

166.  But  it  is  not  plain,  why  the  latter  orbit  is  an 
ellipse  and  the  former  a  circle.  Tc  explain  this,  close 
attention  must  be  given  to  the  direction  of  the  two 
forces,  projectile  and  centripetal.  In  the  first  case, 
when  the  earth  is  supposed  to  move  in  the  circle  ADC, 
these  forces  act  at  right  angles  to  each  other  in  what- 
ever point  of  its  orbit  the  ear*h  may  be.  And  univer- 
sally ivhen  two  forces  act  at  right  angles  to  each  other, 
one ,  does  not  counteract  the  other.  For  example,  the 
projectile  force  would  carry  the  earth  from  Jl  to  B  in 
the  time  that  the  sun  would  draw  it  to  C ;  it  comes  to 
D,  Now  the  point  D  is  as  far  from  the  line  ACS,  as 
B  is ;  consequently  the  projectile  force  has  carried  the 
earth  just  as  far  as  it  would  in  the  same  time,  if  the  sun 
had  not  attracted  it.  So  the  point  D  is  as  far  from  the 
line  AB  as  C  is  ;  consequently  the  sun  has  drawn  the 
earth  through  just  the  same  space  which  it  would,  if 
there  had  been  no  projectile  force.  The  same  is  true 
in  ev  )ry  part  of  the  circular  orbit ;  and  these  forces 
are  said  to  balance  each  other. 

167.  In  the  second  case,  when  the  earth  is  at.^,  these 
forces  act  at  right  angles;  but  the  projectile  carries  it  to 
B,  while  the  centripetal  would  bring  it  only  to  c.  Con- 
sequently it  comes  to  d,  and  hence  tog,  &c.  But  when 
the  earth  is  at  d,  it  is  plain  that  the  projectile  and  cen- 
tripetal forces  do  not  act  at  right  angles ;  but  the  sun's 
attraction  tends  to  draw  the  earth  backward,   and  to 


92         Motion  of  Heavenly  Bodies  in  their  Orbits. 

prevent  it  from  going  as  far  in  the  second  portion  of 
time  as  it  went  in  the  first;  the  distance  dg  being  less 
than  A  d.  This  effect  becomes  more  and  more  appa- 
rent, till  the  earth  completes  half  its  orbit  at  q.  During 
this  part  of  the  orbit,  the  projectile  force  more  than 
balances  the  sun's  attraction.  But  the  sun's  attraction 
is  constantly  diminishing  that  force  ;  till  at  q,  the  sun's 
attraction  more  than  balances  it,  and  the  earth  begins 
to  approach  the  sun.  At  q,  these  forces  act  again  at 
right  angles;  but  the  projectile  force  being  overba- 
lanced would  carry  the  earth  to  o,  while  the  sun's  at- 
traction would  bring  it  to  r  ;  it  consequently  comes  to 
m.  At  this  point  these  forces  do  not  act  at  right  angles  ; 
but  the  sun's  attraction  tends  to  increase  the  projectile 
force.  And  this  efi^ect  is  more  and  more  obvious  till 
the  earth  comes  to  A  again,  and  these  forces  act  at 
right  angles.  In  this  manner,  the  planets,  primary  and 
secondary,  continually  describe  elliptical  orbits. 

168.  Since  all  attraction  is  mutual,  it  is  obvious  that 
the  sun  does  not  remain  entirely  at  rest,  while  the  earth 
performs  its  revolution  ;  but  must  also  perform  a  small 
revolution  round  the  centre  of  gravity,  which  (on  ac- 
count of  the  smallness  of  the  earth)  cannot  be  far  from 
the  sun's  centre.  In  this  revolution,  it  is  also  manifest 
that  the  sun's  motion  must  be  very  irregular*'  For 
while  the  earth  is  drawing  him  one  way,  some  of  the 
other  planets  are  drawing  him  in  an  opposite  or  side 
direction. 

169.  In  like  manner,  while  the  moon  performs  its 
revolution  round  the  earth,  the  earth  also  describes  a 
similar  revolution  round  the  centre  of  gravity.  But  as 
the  difference  in  the  solid  contents  and  distance  of  these 
two  bodies,  is  no  way  comparable  with  that  of  the  sun 
and  earth,  the  centre  of  gravity  is  not  very  near  the 
earth's  centre,  but  is  about  2  000  miles  from  the  earth's 
surface. 


Motion  of  Heavenly  Bodies  m  their  Orbits.  93 

170.  But  the  planets  of  our  solar  system  are  not 
the  only  bodies  which  have  orbits.  It  was  stated  above, 
JVb.  50,  that  many  stars,  which  appear  single  to  the 
naked  eye,  appear  double,  treble,  or  even  quadruple, 
when  seen  through  a  telescope.  According  to  the 
observations  of  distinguished  astronomers,  it  has  been 
found  thai  in  many  cases  the  stars,  composing  these 
double  stars^change  their  situation  with  regard  to  each 
other  )  and  fience  it  is  inferred  that  they  revolve  round 
a  common  centre  of  gravity.  Dr.  Herschel,  during  a 
series  of  observations  on  double  stars^has  found  that  in 
more  than  fifty  of  them,  this  change  of  situation  really 
takes  place  i  and  that  therefore  they  describe  orbits 
round  a  centi*e  of  gravity.  Some  of  their  periodical 
times  he  has  calculated  ;  but  the  accuracy  of  his  cal- 
culations remains  to  be  tested. 

171.  Besides  these  motions  of  the  single  stars  com- 
posing double  ones,  it  is  beyond  question  that  many  of 
the  other  stars  have  motions  peculiar  to  themselves. 
An  apparent  change  of  place  in  some  of  the  stars  was 
first  discovered  by  Dr.  Halley,  (by  comparing  their 
present  places  with  their  places  a^  laid  down  in  ancient 
catalogues.)  Other  astronomers  confirmed  his  obser- 
vations, and  this  motion  of  the  stars  is  termed  their 

^proper  motion, 

■  172.  If  the  stars  be  suns  and  have  motion,  does  our 
sun  also  have  motion  ?  If  so,  the  whole  solar  system 
of  planets,  primary  and  secondary,  must  partake  of  his 
motion,  and  be  canied  along  with  him.  It  will  be 
obvious  on  a  moment's  reflection,  that  if  we  are  moving 
tow  ards  one  part  of  the  visible  heavens,  the  stars  in  that 
quarter  will  appear  to  recede  from  each  other ;  while 
those  in  the  opposite  part,  from  v,  hich  we  are  moving, 
will  appear  to  approach  each  other.  Now  observation 
shows  that  the  stars  in  one  region  of  the  heavens  do 
actually  appear  to  recede  from  each  other,  while  those 
9* 


94  Retrograde  .Motion  of  the  Jloon's  \odes. 

in  the  opposite  region  appear  to  draw  nearer  together. 
Hence  we  seem  to  have  evidence  Httle  short  of  demon- 
stration, that  the  sun  and  we  with  him  are  in  a  progres- 
sive motion.  The  constellation  Hercules  is  the  region, 
to  which  this  motion  appears  to  be  directed. 

173.  If  the  stars  and  the  sun  have  motion,  if  they 
describe  orbits,  around  what  do  they  move  ?  Hitherto 
we  have  stated  only  observations  and  the  conclusions 
resulting  from  them.  But  here  observation  has  not 
been  continued  for  a  length  of  time  sufficient  to  justify 
even  a  conjecture.  All  is  speculation.  Herschel  su|> 
poses  (and  the  supposition  has  simplicity  and  beauty, 
and  hence  probably  truth)  that  the  sun  is  one  of  an  in- 
numerable multitude  of  stars  composing  the  milky-way; 
tJiat  all  these  stars  with  their  systems  have  a  motion 
round  a  common  centre  of  gravity.  /  But  where  this 
centre  is,  he  does  not  pretend  to  conjecture.  (It  is  also 
probable  that  those  whitish  regions  known  as  nebidce, 
(of  which  Dr.  Herschel  has  given  a  catalogue  of  2500.) 
are  each  composed  of  a  systemof  stars  describing  orbits 
round  a  centre  of  gravity,  like  the  stars  of  the  milk\  -wav^ 
Still  the  analogy  of  the  universe  is  not  complete  with(5ut 
^T^iving  these  systems  of  stars,  these  milky-v>avs,  a  pro- 
nrressive  motion;  without  supposing,  tnat  they  describe 
each  an  orbit  round  a  cominon  centre.  But  here  we 
must  stop,  for  no  more  materials  are  given. 


Sect.  II. 


Of  the  retrograde  .Motion  of  the  .Mooirs  \odes, 

174.  Under  the  article  Eclipses,  it  was  stated,  that 
the  moon's  nodes  were  not  always  in  the  same  points  of 
the  ecliptic,  but  had  amotion  backward,  contrary  to  the 
order  of  the  signs ;  by  which  motion  the  line  of  the  nodes 


Of  Irregular  Motions.       '      *  95 

performs  a  complete  revolution  in  little  less  than  19 
years.  It  remains  to  explain  the  cause  of  this  motion. 
175.  The  moon's  orbit  cuts  the  ecliptic  at  an  angle 
of  5 J^ ;  that  is,  the  moon  departs  5  J^  from  the  ecliptic, 
north  and  south.  Let  S  (PI.  VIII,  fig.  2,)  be  the  sun, 
JE  the  earth,  the  line  SE  the  plane  of  the  ecliptic,  the 
line  M  m  the  plane  of  the  moon's  orbit,  and  JW,  m,  the 
moon  in  the  two  opposite  points  of  her  orbit,  where  she 
is  farthest  from  the  ecliptic.  When  the  moon  is  at  m, 
the  sun  draws  it  towards  S,  and  the  earth  towards  E ; 
these  two  attractions  bring  it  downw^ards  tovv  ards  e,  and 
make  it  cut  the  ecliptic  sooner  than  it  would  if  the 
sun  did  not  attract  it.  So  when  the  moon  is  at  M^  the 
moon  draws  the  earth  to  itself,  and  the  sun  to  himself; 
these  two  attractions  tend  to  bring  the  earth  towards  r. 
But  as  the  earth  is  much  larger  than  the  moon,  it  is 
carried  but  little  way  towards  r  ;  but  the  moon  is  car- 
ried in  the  other  direction  towards  a:,  so  that  it  cuts  the 
ecliptic  sooner,  than  if  attracted  by  the  earth  only.  To 
make  this  plainer,  fig.  3  and  4  are  different  views  of 
parts  of  the  ecliptic  and  of  the  moon's  orbit.  JEG  is  a 
part  of  the  ecliptic.  E/T  a  part  of  the  moon's  orbit,  M 
the  moon,  E  a  node.  The  joint  action  of  the  sun  and 
earth  brings  the  moon,  not  to  the  node  E,  but  along  the 
dotted  line  to  r. 


Sect.  III. 

Of  Irregular  Motions. 

176.  Since  attraction  is  mutual  and  varies  according 
to  the  distance  of  the  hodiesy  it  is  obvious  that  in  a  sys 
tem  of  bodies  moving  round  a  common  centre  in  dif- 
ferent  times,  there  must  be    irregular  motions.      For 
example,  since  the  earth  and  Jupiter  move  round  the 


96  Of  Irregular  Motions, 

sun  in  different  times,  they  will  be  nearer  to  each  other 
at  one  time  than  at  another ;  and  consequently  will 
attract  each  other  more  powerfully  at  one  time  than  at 
another.  This  more  powerful  attraction  must  draw 
these  planets  more  or  less  out  of  their  regular  orbits, 
and  thus  disturb  each  other's  motion.  So  also  of  all 
the  planets.  But  it  is  not  very  difficult  to  calculate  the 
principal  disturbing  forces  of  the  planets  on  each  other's 
orbits  and  motions. 

177.  It  was  remarked  at  the  close  of  Sect.  7,  (Chap, 
I.  Book  I,)  that  some  irregularities  in  the  motion  of  the 
old  planets  induced  astronomers  to  suppose  that  a 
planet  existed  between  Mars  and  Jupiter,  long  before 
the  small  new  planets  were  discovered.  Some  disturb- 
ances and  deviations  in  the  motions  of  Jupiter  and 
Saturn  were  also  observed  by  astronomers  before  the 
discovery  of  Uranus,  which  they  could  account  for  only 
by  supposing  them  caused  by  a  planet,  still  more  dis- 
tant from  the  sun  than  Saturn.  It  is  obvious,  that  three 
immense  bodies,  like  Jupiter,  Saturn,  and  Uranus,  re- 
volving at  inconceivable  distances  from  the  centre,  must 
be  very  perceptibly  disturbed  by  the  variation  of  each 
other's  attraction  ;  since  they  are  some  times  three  or 
four  times  nearer  each  other,  than  at  others. 

178.  The  moon  being  a  small  body,  its  motions  are 
greatly  disturbed  and  become  very  irregular  on  account 
of  the  unequal  attractions,  to  which  she  is  exposed. 
Lying  always,  more  than  any  other  heavenly  body,  im- 
der  our  observation ;  and  for  the  purpose  of  calculating 
eclipses  and  for  finding  longitude,  it  being  very  im- 
portant for  us  to  know  her  true  place  ;  astronomers 
have  taken  incredible  pains  to  detect  and  calculate  the 
effects  of  the  forces,  which  disturb  her  motion.  So 
that  now,  to  find  her  true  place  to  a  great  degree  of 
accuracy,  nearly  fifty  corrections  of  her  mean  motion 
become  necessary.    ' 


Of  Irregular  Motions,  97 

179.  In  revolving  round  the  earth,  the  moon  is  some- 
times nearer  the  sun  than  the  earth  is ;  and  sometimes 
farther  off  than  the  earth  is ;  and  is  therefore  disturbed 
by  the  varying  attraction  of  the  sun.  For  example, 
(PL  II,  fig.  3,)  when  the  moon  is  in  or  near  jP,  the 
attraction  of  the  sun  will  make  her  move  faster  than 
she  would  if  attracted  by  the  earth  only ;  because  the 
direction  of  the  sun's  attraction  coincides  more  or  less 
with  the  direction  of  the  moon's  projectile  force  ;  and 
also  because  she  is  nearer  the  sun  and  more  attracted 
by  him  than  the  earth  is.  The  moon  being  thus  acce- 
lerated from  jP  to  A^  continues  to  move  with  something 
more  than  her  mean  velocity,  till  she  comes  to  B ; 
where  it  is  found,  that  she  is  little  more  than  her  own 
diameter  forward  in  her  orbit,  farther  than  she  would 
have  been  had  she  been  attracted  by  the  earth  only. 
But  while  moving  from  B  through  C,  the  sun's  attrac- 
tion tends  to  draw  her  backward  in  her  orbit,  and 
retards  her  motion  just  as  much  as  it  was  accelerated 
before  ;  so  that  when  she  comes  to  jD,  she  is  as  much 
too  slow  in  her  orbit,  as  she  was  too  fast  at  B,  While 
moving  from  D  through  E,  she  is  less  attracted  by  the 
sun  than  the  earth  is  ;  this  produces  the  same  effect  as 
was  produced  in  the  opposite  point  of  her  orbit  at  jP, 
viz,  acceleration  of  her  motion.  Thus,  when  she  comes 
to  /,  she  is  again  too  fast ;  and  when  at  jP  she  is  too 
slow.  (iWlien  the  moon  is  at  B,  D,  /,  ^^  F,  she  is  said 
to  be  in  her  1st,  2d,  2d,  ^  4th  octant  ;  when  at  A,  or 
at  E,  she  is  said  to  be  in  syzygy.)  Hence  it  appears, 
that  the  moon  is  too  fast  in  her  orbit  in  the  1st  &  3d 
octant,  and  too  show  in  the  2d  &  4th.  Also-  that  the 
moon's  motion  is  greater  than  her  mean  motion  in 
syzygy,  and  less  than  her  mean  motion  in  quadrature  ; 
and  that  she  moves  at  her  mean  rate  only  in  the 
octants. 

180.  The  disturbing  force  of  the  sun,  on  the  moon's 


^  Of  Irregular  Motions. 

orbit  and  velocity,  is  obviously  greater  as  the  distance 
of  the  earth  from  the  sun  is  less.  Now  the  earth  is 
nearer  the  sun  vq.  winter  than  in  summer ;  henceTthe 
disturbing  force  of  the  sun  on  the  moon  is  greater 
in  winter  than  in  summoi*.  The  consequence  is,  in 
winter,  when  the  moon  is  at  A^  she  is  drawn  away  from 
the  earth  farther  than  in  summer ;  and  when  at  jE,  the 
earth  is  drawn  away  from  the  moon  more  than  in  sum- 
mer. The  effect  is,  that  the  distance  between  the 
moon  and  earth  is  greater  in  winter  than  in  summer; 
and  hence  the  moon  occupies  a  longer  period  in  com- 
pleting her  revolution  in  the  former  season,  than  in  the 
latter.     The  difference  is  about  24  minutes^ 

181.  It  is  recorded  in  history,  that  an  eclipse  of  the 
moon  took  place  at  Alexandria  on  the  22d  Sept.  201 
years  before  the  Christian  era,  and  that  when  the  moon 
arose,  she  was  so  much  eclipsed,  that  the  eclipse  must 
have  begun  half  an  hour  before  she  rose.  But  accord- 
ing to  our  Tables,  this  eclipse  did  not  begin  till  ten  min- 
utes after  the  moon  rose  at  Alexandria.  Now  had  this 
eclipse  begun  and  ended  while  the  sun  was  below  the 
horizon,  it  might  have  been  supposed  that  the  observer, 
who  had  no  certain  way  of  measuring  time,  might  have 
been  so  far  mistaken  in  the  hours,  that  we  could  not 
rely  on  the  accuracy  of  his  account.  But  as  in  the 
case  given,  the  sun  had  not  set  and  the  moon  had  not 
risen,  till  some  time  after  the  eclipse  began  ;  this  cir- 
cumstance is  such,  that  the  observer  could  not  be  mis- 
taken in  it. 

182.  From  this,  and  many  other  instances  of  dis- 
cordance between  ancient  records  and  our  own  Tables, 
it  is  certain  that  the  moon  now  describes  a  less  orbit, 
and  occupies  less  time  in  a  revolution,  than  she  did 
formerly.  This  fact  led  astronomers,  and  Ferguson 
among  them,  to  suppose  that  the  moon  met  with  some 
resistance  in  her  orbit,  so  that  her  projectile  force  was 


Of  Irregular  Motions.  99 

continually  diminished,  and  her  centripetal  force  in- 
creased.;   They  hence  inferred  that  the  moon  would 
continually   draw   nearer  and   nearer  to  the  earth  by 
slow  degrees,  till  at  length  they  w^ould  fall  together. 
(See  Ferguson'' s  Astronomy^  Nos,  163  and  322 .J 

183.  But  by  examining  the  effects  of  the  several 
planets,  and  especially  of  Jupiter  and  Saturn,  on  the 
form  of  the  earth's  orbit.  La  Place,  an  eminent  French 
astronomer,  has  discovered  that  the  eccentricity  of  the 
earth's  orbit  has  been  diminishing  from  ancient  time ; 
and  that  this  diminution  is  the  cause  of  the  acceleration 
of  the  moon's  motion,  which  we  are  now  considering. 
The  subject  is  too  intricate  to  admit  a  familiar  illus- 
tration ;  but  it  is  important,  as  putting  to  rest  all  those 
fears  of  an  ultimate  wreck  of  this  world,  which  were 
grounded  on  the  apparently  inevitable  effects  resulting 
from  the  principle  of  gravitation.  La  Place  also  dis 
covered  that  this,  and  all  other  irregularities  in  the  Solai 
Sj^stem,  generated  by  the  mutual  action  of  the  planets 
are  all  periodical,  confined  to  narrow  limits,  and  ba 
lanced  by  irregularities  of  an  equal  and  opposite  kind 
After  reaching  a  certain  limit,  they  gradually  diminish, 
till  the  system,  regaining  its  balance,  returns  to  that 
state  of  harmony  and  order,  which  preceded  the  com- 
mencement of  these  secular  inequalities. 

184.  But  there  is  no  class  of  bodies  liable  to  so 
great  disturbances  as.comets.\.The  same  comet  is  some- 
times twice  as  far  distant  from  the  sun  as  Uranus,  and 
in  a  different  part  of  its  orbit,  twice  as  near  to  him 
as  we  are.  Hence  the  motion  of  these  bodies  is  very 
variable.  They  cross  the  orbits  of  the  planets  in  all 
directions;  and  are  of  course  accelerated,  retarded, 
and  turned  out  of  their  course,  according  as  they  actu- 
ally approach  these  bodies.  Dr.  Halley  computed  that 
the  disturbing  power  of  Jupiter  alone  on  the  comet  of 
1682,  would  retard  its  return  511  days;  and  Clairaul 


loo  Of  Irregular  Motions, 

computed  that  that  of  Saturn  would  retard  it  100  days, 
making  together  nearly  a  year  and  three  quarters. 
And  the  event  proved  that  these  computations  were 
very  accurate. 

185.  Though  comets  are  sensibly  disturbed  by  the 
planets,  we  have  not  the  same  evidence,  that  the  planets 
are  ever  sensibly  disturbed  by  them;  probably  owing 
to  their  being  generally  very  small  and  rare  bodies, 
consisting  of  very  little  solid  substance.  In  1454,  the 
moon  is  said  to  have  been  eclipsed  by  a  comet,  which 
therefore  must  have  been  very  near  both  to  the  moon 
and  earth.  Yet  it  produced  no  sensible  effect  on 
either  of  these  bodies  ]  there  being  no  perceptible 
deviation  from  their  accustomed  path  round  the  sun. 
The  comet  of  1770  came  so  near  the  earth,  that  La 
Place  computed,  that  its  periodical  time  would  be 
increased  by  tiie  disturbing  action  of  the  earth  some- 
thing more  than  two  days  ;  and  if  its  solid  contents  had 
equalled  those  of  the  earth,  it  was  calculated  that  it 
would  have  retarded  the  earth's  motion  in  her  orbit, 
and  thereby  have  lengthened  our  year,  2  hours  and 
48  minutes.  It  is  certain  that  no  such  increase  took 
place  ]  and  therefore  the  disturbing  force  of  the  comet 
on  the  earth  was  insensible.  The  same  comet  passed 
through  the  midst  of  Jupiter's  satellites. 

We  have  stated  that  in  ancient  times  comets  were  looked  upon 
with  terror  as  harbingers  of  evil.  Their  appearance  and  disappear- 
ance were  phenomena  totally  unaccountable.  But  when  Newton 
had  developed  the  laws  of  their  motion,  and  had  assigned  them 
their  true  place  in  the  Solar  System,  the  superstitious  fear  of  the 
ancients  gave  way  to  the  philosophical  fear  of  the  moderns;  a  fear, 
which  (for  all  that  we  can  see)  must  ever  harass  the  mind,  which 
is  not  disposed  to  acknov/ledge  a  Supporter  and  Governor  of  the 
universe  as  well  as  a  Maker  of  it.  When  it  was  ascertained,  that 
a  great  number  (none  can  tell  how  many)  of  these  bodies  were 
continually  moving  in  all  directions  through  the  different  regions 
of  our  planetary  system,  it  was  apprehended  that  some  of  them 
might  meet  the  earth  in  its  course,  and  thereby  produce  a  shock, 


spheroidal  Figure  of  the  Planets,  10 i 

which  might  be  nearly  or  quite  destructive  to  the  hun^an  race. 
Imagination  was  let  loose  ;  and  most  of  the  great  physical  evils, 
which  our  race  are  said  to  have  suffered,  and  the  most  direful 
which  they  can  look  forward  to,  have  been  traced  with  ingenuity 
to  comets.  So  that  long  after  the  law  of  their  motions  was  well 
known  and  understood,  the  appearance  of  a  comet  excited  juster 
(because  more  definite)  fear  in  the  breast  of  the  philosopher,  than 
in  the  ancient  peasant.  Nor  is  this  fear  yet  removed.  Astrono- 
mers, it  is  true,  have  calculated  the  chances  of  collision  between 
the  earth  and  a  comet,  and  have  found  the  chance  greatly  against 
such  an  event.  But  according  to  their  calculation,  there  is  a 
chance  of  such  an  event ;  and  while  this  is  admitted,  there  must 
be  fear  that  it  will  take  place.  This  fear  probably  pervades  most 
people  more  or  less ;  and  while  we  are  confined  to  philosophy,  and 
philosophy  developes  no  new  laws  of  motion,  it  is  unavoidable,  and 
can  be  resisted  and  overcome  only  by  a  full  belief,  that  there  is  a 
Divine  Providence  overruling  and  directing  all,  even  the  most  mi 
nute  operations,  which  are  exhibited  to  us  in  the  natural  world. 
There  can  be  no  occasion  for  fear  of  any  effects  resulting  from  ope 
rations,  which  we  acknowledge  to  be  directed  and  governed  by 
divine  wisdom,  which  sees  the  end  from  the  beginning ;  and  the 
design  of  which^  we  feel  assured,  is  the  welfare  and  happiness  of 
man. 


Sect.  IV. 


Of  the  Spheroidal  Figure  of  the  Earth  and  other 
Planets. 

186.  It  has  been  stated,  that  as  a  body  moves  faster, 
Its  tendency  to  move  in  a  straight  line  is  greater.  Now 
if  two  bodies  describe  unequal  circles  in  the  same  time, 
as  in  one  day,  the  body  which  describes  the  largest  cir- 
cle must  manifestly  move  faster,  than  the  body  which 
describes  the  least ;  consequently,  its  continual  ten- 
dency to  move  in  a  straight  line  is  greater  than  that  of 
the  other.  For  example,  (PL  IX,  fig.  3,)  if  a  body 
at  A  describe  the  circle  J.  a,  in  the  same  time  that  a 
body  at  B  does  the  circle  B  b,  the  bodv  at  A  must 
obviously  move  faster  than  that  at  IJ ;  and  consequently 
10  ^         J 


1 02  Spheroidal  Figure  of  the  Planets. 

It  tends,  in  every  part  of  the  circle,  to  move  in  a  straight 
line  more  than  that  at  B  does. 

187.  Now  the  parallels  of  latitude;  (PI.  II,  fig.  1,) 
on  the  globe,  are  circles  of  different  lengths.  The 
equator  is  the  greatest  circle,  and  parallels  diminish 
towards  the  poles.  Hence  those  bodies,  which  lie  on 
or  near  the  equator,  are  carried  by  the  earth's  rotation 
on  its  axis  through  larger  circles  in  a  day,  than  bodies 
lying  near  the  poles.  Whence  it  follows,  that  bodies 
near  the  equator  have  a  greater  tendency  to  move  in 
straight  lines,  and  consequently  to  recede  farther  from 
tli^  eartKs  centre^  than  bodies  near  the  poles  ;  while  at 
the  poles  this  tendency  entirely  ceases. 

188.  Were  the  earth  composed  of  a  liquid,  as  water, 
it  is  hence  plain  what  would  be  its  form.  By  rotation 
on  its  axis,  the  parts  about  the  equator  would  swell 
outward,  while  the  regions  about  the  poles  would  be 
somewhat  depressed  and  flattened.  It  would  take  some- 
thing of  the  form  of  a  flat  turnip,  or  of  two  saucers  put 
together.  Now,  though  the  earth  be  not  a  fluid,  yet  it 
is  not  a  perfectly  solid  mass.  Its  parts  are  not  very 
difficult  of  separation.  By  daily  rotation  it  has  actually 
taken  something  of  the  form,  which  it  would  take  were 
it  a  fluid.  Its  diameter  through  the  equator  is  greater 
than  through  the  poles  by  about  26  miles.  As  most,  if 
not  all  the  heavenly  bodies  turn  on  an  axis,  most,  if  not 
all,  partake  of  the  same  form  as  the  earth. 

189.  There  is  one,  striking  fact  resulting  from  this 
figure  of  the  earth.  Pendulums  vibrate  by  the  force  of 
gravity.  When  propelled  sideways,  gravity  carries  a 
pendulum  back  ;  and  in  carrying  it  back,  gives  it  such 
velocity  as  to  carry  it  as  far  on  the  other  side  ;  whence 
it  returns,  and  is  again  carried  to  the  other  side,  and  so 
on.  As  these  vibrations  are  continued  by  the  force  of 
gravity,  they  must  be  quicker  as  the  force  of  gravity  is 
increased.     For  any  body,  propelled  by  a  greater  force 


Precession  of  the  Equinoxes,  103 

must  move  quicker  than  when  propelled  by  a  less.  Now 
all  bodies  on  the  earth's  surface  are  drawn  to  its  centre ; 
and  more  powerfully,  as  the  square  of  their  distance  is 
less.  Hence,  if  one  portion  of  the  earth's  surface  be 
farther  from  its  centre  than  another,  the  force  of  gravity 
on  a  pendulum  in  one  place  must  be  less  than  in  ano- 
ther ;  and  consequently  the  pendulum  will  vibrate  slower 
in  one  place  than  in  another.  This  is  found  to  be  actu- 
ally the  case.  Pendulums  vibrate  faster  towards  the 
poles,  and  slowest  at  the  equator.  This  eflect  is  con- 
siderably augmented  by  the  centrifugal  force  of  the 
body  being  increased  as  it  approaches  the  equator. 
For  the  same  reasons,  bodies  are  heavier  at  the  poles 
than  at  the  equator. 

Pendulums  of  the  same  length  vibrate  in  the  same  time,  however 
different  in  weight.  Short  pendulums  vibrate  quicker  than  long 
ones.  Pendulums  vibrating  seconds  at  London,  are  39.2  inches  in 
length )  but  at  the  equator  39.1  inch  nearly. 

TABLE 

Shoimng  the  proportion  of  the  Polar  to  the  Equatorial 
Diameters  of  the  Planets  ;  as  far  as  known. 
Earth  .  .  326     to  327 

Mars        .  .  .         15      "      16 

Jupiter  .  .  12 J  ''      13^- 

Saturn      .  .  .         32  .   '*      35 

Sect.  V. 

Of  the  Precession  of  the  Equinoxes, 

190.  It  has  been  stated  that  there  is  a  difference  )be- 
tween  a  solar  and  siderial  year.  A  solar  year  is  mea- 
sured from  the  time  the  earth  sets  out  from  a  particular 
ooint  in  the  ecliptic,  as  an  equinox  or  solstice,  till  it  re- 
}urns  to  the  same  point  again.     This  is  found  to  take 


104  Precession  of  the  Equinoxes, 

place  before  it  completes  its  revolution,  which  is  a  side- 
rial  year.  For  example,  (PI.  IX,  fig.  1,)  if  the  sun  S, 
earth  E,  and  a  star  be  in  the  same  straight  line  at  an 
equinox,  the  earth  revolving  through  «,  will  not  be  at  E 
at  the  same  equinox,  but  somewhere  at  e.  Hence  it 
must  revolve  farther,  from  e  to  E,  before  it  completes 
its  revolution  ;  and  the  time  of  doing  this  is  the  differ- 
ence between  a  solar  and  siderial  year,  and  amounts  to 
about  20  minutes,  f^he  distance  e  jG  is  about  50^^  of  a 
degree  annually,  and  constitutes  what  is  called  the 
precession  cf  the  equinoxes.  I 

191.  The  precession  of  the  equinoxes  is  to  be  ac- 
counted for  in  much  the  same  way  that  the  retrograde 
motion  of  the  moon's  nodes  is.  It  has  been  stated, 
that  the  diameter  of  the  earth  at  the  equator  is  greater 
than  through  the  poles.  Suppose  this  excess  of  matter 
about  the  equator  to  be  a  ring  round  the  earth,  but  se- 
parate from  it,  leaving  the  earth  a  perfect  globe  or 
sphere.  Let  A  b  B  c  (PL  IX,  fig.  2,)  be  a  circle  in 
the  plane  of  the  ecliptic.  Let  ACB  be  half  the  ring 
we  have  su{>posed,  lying  above  the  ecliptic,  and  making 
an  angle  with  it  of  23^^^.  Now  the  efiect  of  the  sun's 
attraction  on  this  ring  is  the  same,  during  a  year, 
whether  we  suppose  the  earth  to  move  round  the  sun, 
or  the  sun  to  move  round  the  earth.  Let  us  then  sup- 
pose the  sun  to  move  round  the  earth  in  the  circle 
ti  SV.  While  the  sun  is  moving  frcm  a  through  S"  to 
V,  that  is,  during  half  the  year,  the  sun  acts  successive- 
ly on  all  the  parts  of  the  ring  from  A  though  C  to  B, 
This  action  tends  to  draw  the  ring  into  the  plane  of  the 
ecliptic ;  and  the  effect  is  such  as  to  make  it  cut  the 
ecliptic  somewhere  at  x,  and  not  at  i?,  Vvhere  it  did 
before.  So  while  the  sun  is  going  the  other  half  of  its 
orbit,  it  acts  in  the  same  manner  on  the  other  half  of 
the  ring  ;  and  makes  it  cut  the  ecliptic  somewhere  at 
d  instead  of  ./J      Thus   the   equinoxes  are  constantly 


Of  the  Tides,  105 

shifting  backward.  For  the  effect  we  have  supposed 
on  this  ring,  detached  from  the  earth,  actually  takes 
place  while  it  is  attached  to  the  earth,  and  forms  a  part 
of  it. 

192.  As  the  equinoctial  points  move  backward,  and 
the  sign  Aries  always  begins  at  one  of  them,  and  all  the 
other  signs  of  30^  each  follow  Aries  in  order,  it  follows 
that  all  the  signs  of  the  ecliptic  or  zodiac  move  back- 
ward with  the  equinoxes.  Consequently  stars,  which 
are  in  one  sign  at  one  time,  will  be  in  the  succeeding 
one  at  another.  Hence  comes  the  fact  spoken  of  No. 
54.  The  sign  Aries  nearly  coincides  with  the  constel- 
lation Pisces ;  and  Taurus  with  the  constellation  Aries^ 
and  so  on.  When  these  names  were  given  to  the  signs 
and  constellations,  probably  each  sign  coincided  with 
the  constellation  of  the  same  name ;  but  on  account  of 
the  precession  of  the  equinoxes,  there  is  now  about  one 
sign  or  30°  difference.  In  about  2000  years  there  will 
be  a  difference  of  two  signs  or  60°. 


Sect.  VI. 

Of  the  Tides, 

193.  Oceans  are  observed  to  have  a  regular  rising 
and  falling  of  their  waters,  v/hich  are  called  tides. 
There  are  two  tides  in  about  25  hours.  These  are 
occasioned  by  the  attraction  of  the  moon ;  but  affected 
also  by  that  of  the  sun. 

194.  Let  JIf  (PL  IX,  fig.  4,)  be  the  moon  revolving 
in  its  orbit  ;  E  the  earth  covered  with  water.  The 
moon,  drawing  the  earth  to  itself,  affects  the  solid  parts 
of  it,  just  as  if  its  whole  weight  were  in  a  single  point  in 
or  near  the  centre  E,  Now  the  waters  at  A  are  near- 
er the  moon  than  the  point  E,  and  are  consequently 


(06  Of  the  Tides, 

more  attracted  than  the  earth.  Hence  the  waters  are 
heaped  up  under  the  moon  at  .4.  But  the  waters  on 
the  opposite  side  at  B  are  less  attracted  than  the  earth ; 
consequently  the  earth  is  drawn  away  from  them,  and 
they  are  heaped  up  at  B.  When  the  waters  are  heap- 
ed up  at  .A  and  Z?,  it  is  plain  they  must  recede  from  the 
intermediate  points  C  and  D. 

195.  Thus  while  the  earth  turns  on  its  axis,  any  par- 
ticular place  as  Jl  has  two  tides,  v>'hile  passmg  from 
under  the  moon  till  it  comes  under  the  moon  again. 
But  while  the  earth  is  turning  on  its  axis,  the  moon  ad- 
vances in  its  orbit,  so  that  the  earth  must  a  little  more 
than  complete  its  rotation  before  the  place  A  comes 
under  the  moon.  This  makes  high  or  low  water  at  any 
place  about  50  minutes  later  one  day  than  on  the  pre- 
ceding. 

196.  It  is  obvious,  that  the  waters  directly  under 
the  moon  are  nearer  to  it  than  those  any  where  else  ; 
consequently  are  more  attracted.  And  as  the  moon's 
orbit  differs  but  little  from  the  ecliptic,  the  moon  can- 
not be  but  about  29°  from  the  equator,  generally  it  is 
much  less.  Hence  the  waters  about  the  equator  are 
more  attracted,  and  of  course  the  tides  are  higher  than 
towards  the  poles.  At  or  near  the  poles  tides  must 
cease. 

197.  The  sun  attracts  the  waters  as  well  as  the  moon. 
But  the  difference  between  the  distance  of  the  centre 
and  surface  of  the  earth  from  the  s^m,  compared  with 
the  whole  distance  of  the  earth  from  the  sun,  is  so 
small,  that  the  sun  acts  on  the  waters  very  nearly  as  it 
does  on  the  solid  land/;  and  consequently  produces  lit- 
tle tide.  When  the  moon  is  at  full  or  change,  it  acts 
with  the  sun ;  that  is,  the  sun  and  moon  tend  to  raise 
tides  at  the  same  places.  Hence  tides  are  then  very 
high,  and  are  called  spring  tides.:  But  when  the  moon 
is  in  quadrature  (PI.   IX,  fig.   5,)  the  sun  and  moon 


Of  the  Tides.  lOt 

tend  to  raise  tides  at  different  places,  and  counteract 
each  other's  effects.  The  moon  raises  tides  at  C  and 
D,  and  the  sun  tends  to  raise  them  at  A  and  B,  But 
the  sun  does  not  raise  tides ;  its  only  effect  is  to  di- 
minish or  increase  those  of  the  moon.  (Tides,  when 
the  moon  is  in  quadratures,  are  very  low)  and  are  called 
neap  tides. 

198.  As  the  sun  is  always  in  the  ecliptic,  and  of 
course  is  never  more  than  23J°  from  the  equator,  tiis 
influence  is  joined  with  that  of  tlie  moon  in  making 
tides  high  at  the  equator,  and  lower  towrirds  the  poles. 
Hence,  if  the  earth  were  a  perfect  globe,  and  had  no 
excess  of  matter  nearer  the  equator,  the  constant  ac- 
tion of  the  sun  and  moon  on  the  waters  of  the  ocean 
would  keep  the  equatorial  region  constantly  immersed. 

199.  But  spring  tides  are  not  always  equally  high  at 
the  same  place.  When  k^q  sun  and  moon  are  in  the 
equator,  their  combined  effect  on  the  w^ater  is  great- 
est) This  is  at  the  time  of  the  equinoxes.  But  as  the 
earth  is  nearer  the  sun  in  winter  than  in  summer,  and 
thereby  the  sun's  action  is  increased,  therefore  our 
highest  spring  tides  are  usually  a  little  after  the  autum- 
nal equinox,  and  little  before  the  vernal. 

200.  It  is  to  be  noticed,  that  tides  are  not  at  their 
height  when  the  moon  is  in  the  meridian,  as  would 
appear  from  the  figures  ;  but  tl.is  takes  place  one  or 
tw^o  hours  after  the  moon  has  passed  the  meridian,  be- 
cause she  continues  to  attract  the  water  during  that 
time. 

201.  Besides  the  continually  varying,  co-operating, 
or  contrary  attraction  of  the  sun  and  moon,  there  are 
other  causes  which  affect  the  time  and  height  of  full 
tide.  X  Strong  winds,  blowing  in  a  particular  direction, 
and  for  a  long  time,  produce  currents  in  the  ocean, 
which  greatly  affect  the  regular  tides.  Different  places, 
also  equally  subject  to  the  moon's  action,  will  have  ma- 


108  Of  the  Tides. 

terially  different  tides  ;  owing  to  currents  in  the  ocean, 
to  the  position  of  the  neighbouring  coast,  &c.  Conti- 
nents stop  the  tides  in  their  course  from  cast  to  west ; 
consequently,  tides  are  generally  higher  on  an  eastern 
coast  than  on  a  w^estern.  Thus  it  is  supposed,  that  the 
water  in  the  Gulf  of  Mexico  is  several  feet  higher  than 
on  the  other  side  of  the  isthmus;  and  Kapoleon  says, 
(Voice  from  St,  Helena^)  "I  had  the  Red  Sea  survey- 
ed, and  found  that  the  waters  of  it  were  thirty  feef  high- 
er than  the  Mediterranean  when  the  waters  were  high- 
est, but  only  twenty-four  feet  at  the  lowest."  In  mouths 
of  rivers  and  bays  opening  eastward,  and  growing  nar- 
rower inland,  tides  rise  to  a  great  height.  At  the 
mouth  of  the  Indus,  tides  rise  thirty  feet ;  and  in  the 
bay  of  Fundy,  sometimes  to  the  astonishing  height  of 
sixty  feet.  They  are  rem.arkably  high  on  the  coast  of 
Malay,  in  the  strait  of  Sunda,  and  in  the  Red  Seal  In 
the  Mediterranean  and  Baltic,  which  have  very  narrow 
inlets,  and  open  westward,  scarce  any  tide  is  percepti- 
ble. Hence  the  Greeks  and  early  Romans  were  igno- 
rant that  any  such  phenomenon  existed. 

202.  In  narrow  rivers,  the  tides  are  frequently  very 
high  and  sudden,  from  the  resistance  of  the  banks, 
t  The  tide  is  said  to  enter  the  river  Severn  in  England 
sometimes  with  a  head  ten  feet  in  height.  In  rivers 
w^here  there  are  many  obstructions  arising  from  banks, 
shallow^s,  and  sinuosities,  there  are  not  unfrequently 
several  tides  at  different  places.  Thus  in  the  river 
Thames,  it  is  high  tide  at  London  and  at  the  Nore 
(mouth  of  the  river)  at  the  same  time ;  while  between 
these  places,  there  is  low  tide.  The  same,  according 
to  Dr.  Franklin,  takes  place  in  the  Delaware  river.  In 
the  river  Amazon,  in  South  America,  where  the  tide 
flows  up  500  miles,  it  is  said  there  are  no  fewer  than 
seven  high  tides  at  various  distances,  and  of  course,  low 
tides  between  them,  all  at  the  same  time. 


APPENDIX. 

Sect.  I. 

Of  Meteors. 

203.  Of  the  origin  and  real  nature  of  those  bodies,, 
which  are  known  to  every  one  as  falling  stars  or  me- 
tcors,  and  of  which  many  may  be  seen  during  almost 
every  clear  evening,  we  are  nearly  or  quite  as  ignorant 
as  were  our  progenitors  three  thousand  years  ago.  In- 
stead therefore  of  conjectures  on  these  points,  we  shall 
confine  ourselves  to  the  description  of  a  few  of  the  most 
remarkable  phenomena  of  this  kind. 

204.  Messrs.  Humboldt  and  lionpland  while  at  Cu- 
mana,  in  South  America,  witnessed  a  very  remarkable 
appearance  of  meteors.  The  former  thus  describes 
it: — "The  night  of  the  11th  November,  1779,  was  cool 
and  extremely  beautiful.  Toward  the  morning,  from 
half  after  two,  the  most  extraordinary  luminous  meteors 
were  seen  towards  the  east.  Bonpland,  who  had  risen 
to  enjoy  the  freshness  of  the  air  in  the  gallery,  perceiv- 
ed them  first.  Thousands  of  bolides  (fire-balls)  and 
falling  stars,  succeeded  each  other  during  four  hours. 
Their  direction  was  very  regular  from  north  to  south. 
They  filled  a  space  in  the  sky  extending  from  the  true 
east  30^  towards  the  north  and  south.*  Some  of  them 
attained  a  height  of  40^ ;  and  all  exceeded  25^  or  30^. 
There  was  very  little  wind,  and  no  trace  of  clouds  to 
be  seen.  Bonpland  relates,  that  from  the  beginning  of 
tne  phenomenon,  there  was  not  a  space  in  the  firma- 
ment equal  in  extent  to  three  diameters  of  the  moon, 
vyliicli  was  not  filled  at  every  instant  vv^ith  bolides  and 
liuruig  stars.  » AH  these  meteors  left  luminous  traces 
ir;>in  >)    to  10'^  in  length;  and  the  phosphorescence  of 


no  Of  Meteors. 

these  traces,  or  luminous  bands,  lasted  seven  Or  eight 
seconds.  The  bolides  seemed  to  burst  as  by  explosion  ; 
but  the  largest,  those  from  1°  to  1^  15'  in  diameter 
(the  mean  diameter  of  the  sun  is  30'  42'',J  disappeared 
without  scintillation,  leaving  behind  them  phosphores- 
cent bands,  exceeding  in  breadth  15'  or  20'. 

205.  "  These  bolides  were  visible  at  the  same  time 
on  the  frontiers  of  Brazil,  a  distance  of  230  leagues 
from  Cumana.  I  was  therefore  powerfully  struck  at 
the  immense  height,  which  they  must  have  attained. 
Put  what  was  my  astonishment,  when  at  my  return  to 
Europe,  I  learnt,  that  the  same  phenomenon  had  been 
perceived  on  an  extent  of  the  globe  of  64°  of  latitude, 
and  91°  of  longitude  ;  at  the  equator  in  South  America, 
at  Labrador  and  Greenland,  and  in  Germany ! 

206.  "A  phenomenon  analogous  to  that  of  the  12th 
of  November,  was  observed  thirty  years  before,  on  the 
table  land  of  the  Andes,  in  a  country  studded  with  vol- 
canoes. At  the  city  of  Quito,  there  was  seen,  in  one 
part  of  the  sky,  above  the  volcano  of  Gayamba,  so 
great  a  number  of  falling  stars,  that  the  mountain  was 
thought  to  be  in  flames.  This  singular  sight  lasted 
more  than  an  hour.  The  people  assembled  in  the  plain 
of  Exico,  where  a  magnificent  view  presents  itself  of 
the  highest  summit  of  the  Cordilleras.  A  procession 
was  already  on  the  point  of  setting  out  from  the  con- 
vent of  St.  Francis,  when  it  was  perceived,  that  the 
blaze  of  the  horizon  was  caused  by  fiery  meteors, 
which  ran  along  the  skies  in  rJl  directions,  at  the  alti- 
tude of  12°  or  13°." 

207.  Meteors  are  often  seen  and  heard  to  burst ;  and 
the  explosion  is  not  unfrequently  followed  by  the  fall 
of  masses  of  stone.  These  are  denominated  Aerolites. 
They  often  descend  with  such  force  as  to  bury  them- 
selves several  feet  in  the  earth.  Cardan  tells  us,  mat 
in  1510,  a  great  fire  was  seen  in  the  heavens  about 


Of  Meteors    _  IJl 

three  o'clock,  and  stones  fell  about  fivo  o'clock.  He 
adds,  that  he  himself  saw  120  stones  fall:  of  which  one 
weighed  120  pounds,  and  another  sixty.  It  is  related 
by  Dr.  Halley,  that  on  the  21st  May,  1676,  a  fire-ball 
was  seen  to  come  from  Dalmatia,  proceeding  over  the 
Adriatic  sea ;  it  passed  obliquely  over  Italy,  where  a 
hissing  noise  was  heard.  It  burst  S.  S.  W.  from  Leg- 
horn, with  a  terrible  report,  and  the  pieces  are  said  to 
have  fallen  into  the  sea  with  the  same  sort  of  noise,  as 
when  red  hot  iron  is  immersed  in  water. 

A  very  particular  and  intti'esting  account  of  JVLeteors 
and  Aerolites  may  he  found  in  Wonders  of  the 
World,  an  American  edition  of  which  has  recently  been 
published. 

We  shall  close  this  section  with  an  account  oi  a  meteor  which 
was  seen  in  various  parts  of  New  England  on  the  morning  of  the 
14th  of  December,  1807;  and  which  burst  near  the  town  of  Weston, 
in  Connecticut.  The  facts  relating  to  it  were  collected  and  arrang- 
ed by  Professors  Silliman  and  Kingsley,  and  published  in  the  Ame- 
rican Register,  Vol.  II ;  from  which  work  the  following  account  is 
collected : — 

"  This  meteor,  which  excited  alarm  in  many,  and  astonishment  in 
all,  first  made  its  appearance  in  Weston,  about  a  quarter  or  half  past 
six  o'clock,  A.  M.,  on  Monday,  the  l4th  Dec.  The  day  had  merely 
dawned,  and  there  was  little  or  no  light,  except  from  the  moon, 
which  was  just  setting.  Judge  Wheeler  was  passing  through  the  en- 
closure adjoining  his  house,  witJi  his  face  to  the  north,  and  his  eyes 
on  the  ground,  when  a  sudden  flash,  occasioned  by  the  transition  of 
a  luminous  body  across  the  northern  margin  of  the  clear  sky,  illumi- 
nated every  object,  and  caused  him  to  look  up.  He  immediately  dis- 
covered a  globe  of  fire,  just  then  passing  behind  a  cloud,  which  was 
very  dark  and  obscure,  although  it  did  not  entirely  hide  Clie  meteor. 

"  In  this  situation  its  appearance  was  distinct  and  well  defineo,  like 
that  of  the  sun  seen  throuoh  a  mist.  It  appeared  about  one  half  or 
two  thirds  the  diameter  of  the  full  moon.  This  description  of  its  ap- 
parent magnitude  is  vague,  but  it  was  impossible  to  ascertain  what 
angle  it  subtended.  Its  progress  was  not  so  rapid  as  that  of  common 
meteors  and  shooting  stars.  When  it  passed  behind  the  thinner 
clouds,  it  appeared  brighter  than  before;  and  when  it  passed  the 
spots  of  clear  sky,  it  flashed  v^^ith  a  vivid  light,  yet  not  so  intense  as 
the  lightning  in  a  thunder  storm,  but  rather  like  what  is  commonly 
called  heat  lightning.     Its  surface  was  apparently  convex. 

"  Where  it  was  not  too  nmch  obscured  by  thick  clouds,  &,  conical 
train  of  paler  light  was  seen  to  attend  it  waving,  and  in  length  about 


112  Of  Meteors,    ^ 

ten  or  twelve  diameters  of  the  body.     In  the  clear  sky  a  brisk  scin- 
tillation was  observed  about  the  body  of  the  meteor,  like  that  of  a 

burning  fire-brand  carried  against  the  wind. 

'*  It  disappeared  about  fifteen  degrees  short  of  the  zenith,  and  about 
the  same  number  of  degrees  west  of  the  meridian.  It  did  not  vanish 
instantaneously,  but  grew,  pretty  rapidly,  fainter  and  fainter,  as  a 
red  hot  cannon  ball  would  do,  if  cooling  in  the  dark,  only  with 
much  more  rapidity.  When  the  meteor  disappeared,  there  were  ap- 
parently three  successive  efforts  or  leaps  of  the  fire-ball,  which  grew 
more  dim  at  every  throe,  and  disappeared  with  the  last. 

*'  There  was  no  peculiar  smell  in  the  atmosphere,  nor  were  any 
luminous  masses  seen  to  separate  from  the  body.  The  whole  period 
between  its  first  appearance  and  total  extinction  was  estimated  at 
^bout  thirty  seconds. 

*'  About  thirty  or  forty  seconds  after  this,  three  loud  and  distinct  re- 
ports, like  those  of  a  four  pounder  near  at  hand,  were  heard.  They 
succeeded  each  other  with  as  much  rapidity  as  was  consistent  with 
distinctness,  and  all  together  did  not  occupy  three  seconds.  Then 
followed  a  rapid  succession  of  reports  less  loud,  and  running  into 
each  other,  so  as  to  produce  a  continued  rumbling,  like  that  of  a  can- 
non ball  rolling  over  a  floor,  sometimes  louder,  and  at  other  times 
fainter  ;  some  compared  it  to  the  noise  of  a  waggon,  running  rapidly 
down  a  long  and  stony  hill  ;  or,  to  a  volley  of  musketry,  protracted 
into  what  is  called,  in  military  language,  a  running  fire. 

"  We  proceed  to  detail  the  consequences  which  followed  the  ex- 
plosions and  apparent  extinction  of  this  luminary.  We  allude  to  the 
fall  of  a  number  of  masses  of  stone  in  several  places,  principally  with- 
in the  town  of  Weston.  The  places  which  had  been  w^ell  ascertain- 
ed at  the  period  of  investigation  were  six.  The  most  remote  were 
about  nine  or  ten  miles  distant  from  each  other,  in  a  line  differing 
little  from  the  course  of  the  meteor.  It  is  therefore  probable  that  the 
successive  masses  fell  in  this  order,  the  most  northerly  fiist,  and  Xhc- 
most  southerly  last.  We  think  we  are  able  to  point  out  three  prin- 
cipal places  where  stones  have  fallen,  corresponding  with  the  three 
loud  cannon-like  reports,  and  with  the  three  leaps  of  the  meteor. 
There  were  some  circumstances  common  to  all  cases.  There  was 
in  every  instance,  immediately  after  the  explosions  had  ceased,  a 
loud  whizzmg  Or  roaring  noise  in  the  air,  observed  at  all  the  places, 
and,  so  far  as  was  ascertained,  at  the  moment  of  the  fall.  It  excited 
m  s^  me  the  idea  of  a  tornado,  in  others  of  a  large  cannon-shot  in  ra- 
pid motion ;  and  it  filled  all  with  astonishment  and  apprehension  of 
some  impending  catastrophe.  In  every  instance,  immediately  after 
this,  was  heard  a  sudden  and  abrupt  noise,  like  that  of  a  ponderous 
body  striking  the  ground  in  its  fall.  Excepting  one,  the  stones  vrere 
more  or  less  broken.  The  most  important  circumstances  of  the 
particular  cases  were  as  follows  : — 

'•  1.  The  most  northerly  fall  was  within  the  limits  of  Huntins-ton, 
on  the  border  of  Weston,  contiguous  to  the  house  of  Mr.  JVlerv.in 
liurr.     Mr.  Burr  was  standing  in  the  road  in  front  of  his  house  v.  hen 


Of  Meteors.  113 

the  stone  fell.  The  noise  produced  by  its  collision  with  a  rook  of 
granite,  on  which  it  struck,  was  very  loud.  Mr.  Burr  was  within 
fifty  feet,  and  immediately  searched  for  the  body,  but,  it  being  still 
dark,  he  did  not  find  it  till  half  an  hour  after.  By  the  fall  some  of  it 
was  reduced  to  powder,  and  the  rest  of  it  was  broken  into  very  small 
fragments,  which  were  thrown  around  to  the  distance  of  twenty  or 
thirty  feet.  The  granite  rock  was  stained  at  the  place  of  contact 
with  a  deep  lead  colour.  The  largest  fragment  which  remained  did 
not  exceed  the  size  of  a  goose  Ggtr,  and  this,  Mr.  Burr  found  to  be 
still  warm  to  his  hand.  There  was  reason  to  conclude,  from  all  the 
circumstances,  that  this  stone  must  have  weighed  about  twenty  or 
twenty-five  pounds 

''  2.  The  masses  projected  at  the  second  explosion  seem  to  have 
fallen  prircipally  at  and  in  the  vicinity  of  Mr.  William  Prince's  in 
Weston,  distant  about  five  miles,  in  a  southerly  direction,  from  Mr. 
Burr's.  Mr.  Prince  and  family  were  still  in  bed,  v.hen  ihey  I/card  a 
noise  like  the  fall  of  a  very  heavy  body  imviediatchj  after  the  ex- 
plosions.  They  formed  various  unsatistactory  conjectures  concern- 
ing the  cause,  nor  did  even  a  fresh  hole  made  through  the  turf  in  the 
door  yard,  about  twenty-five  feet  from  the  house,  lead  to  any  con- 
ception of  the  cause,  or  induce  any  other  inquiry  than  why  a  new 
post  hole  should  have  been  dug  where  there  was  no  use  for  it.  So 
far  were  this  family  from  conceiving  of  the  possibility  of  such  an 
event  as  stones  falling  from  the  clouds.  They  had  indeed  formed  a 
vague  conjecture  that  the  hole  might  have  been  made  by  lightning, 
but  would  probably  have  paid  no  further  aUention  to  the  circumstance 
had  they  not  heard,  in  the  course  of  the  day,  that  stones  had  fallen 
that  morning  in  other  parts  of  the  town.  This  induced  them,  towards 
evening,  to  search  the  hole  in  the  yard,  where  they  found  a  stone  bu- 
ried in  the  loose  earth  which  had  fallen  in  upon  it.  It  was  two  feet 
from  the  surface  ;  the  hole  was  about  twelve  inches  in  dianjeter  ;  and 
as  the  earth  was  soft  and  nearly  free  from  stones,  the  mass  had  sus- 
tained little  injury,  only  a  few  small  fragments  having  been  detached  by 
the  shock.     The  weight  of  this  stone  was  about  thirty-five  pounds. 

"  Six  days  after,  another  mass  was  discovered,  half  a  mile  north- 
west from  Mr.  Prince's.  It  was  in  small  fragments,  having  fallen  on 
a  globular  detached  mass  of  gneiss  rock,  which  it  split  in  two,  and 
by  which  it  was  itself  shivered  to  pieces. 

"  Another  mass  of  thirteen  pounds  weight  had  fallen  half  a  mile 
to  the  north  cast  of  Mr.  Prince's  Having  fallen  in  a  ploughed  field, 
without  commg  into  contact  with  a  rock,  it  was  broken  only  in  two 
principal  pieces,  one  of  which,  possessing  all  the  characters  of  the 
stone  in  a  remarkable  degree,  was  purchased:  for  it  had  now  be- 
come an  article  of  sale.  It  was  urged  that  it  pleased  Heaven  to  rain 
down  this  treasure  upon  them,  and  they  would  bring  their  thunder- 
bolts to  the  best  market  they  could.  This  was,  it  must  be  confessed, 
a  wiser  mode  of  managing  the  business  than  that  which  had  been 
adopted  by  some  others,  at  an  earlier  period  of  these  discoveries. 
Strongly  impressed  with  the  idea  that  these  stones  contained  pold 
11 


1 14  Of  Meteors, 

and  silver,  they  subjected  them  to  all  the  tortures  of  ancient  alche- 
my, and  the  goldsmith's. crucible,  the  forge,  and  the  blacksmith's 
anvil,  were  employed  in  vam  to  elicit  riches  v»iiich  existed  cnly  in 
the  imagination. 

"  It  is  probable  that  these  stones  last  described  were  all  projected 
at  the  second  explosion. 

"  3.  Last  of  all,  we  hasten  to  what  appears  to  have  been  the  catas- 
trophe of  this  wonderful  phenomenon. 

"  A  mass  of  stone  far  exceeding  the  united  weight  of  all  which 
has  been  hitherto  described,  fell  in  a  field  belonging  to  Mr.  Elijah 
Seely,  and  within  thirty  rods  of  his  house. 

"  A  circumstance  attended  the  fall  of  this,  which  seems  to  have 
Dcen  peculiar.  Mr.  Elihu  Staples,  a  man  of  integrity,  lives  en  the 
hill,  at  the  bottom  of  which  this  body  fell,  and  witnessed  the  first 
appearance,  progress  and  explosion  of  the  njeteor.  After  the  last  ex- 
plosion, a  rending  noise,  like  that  of  a  whirlwind,  passed  along  to  the 
east  of  his  house,  and  immediately  over  his  orchard,  which  is  on  the 
declivity  of  the  hill.  At  the  same  instant  a  streak  of  li^ht  pnsscd 
over  the  orchard  in  a  large  curve,  and  seemed  to  pierce  the  ground.  A 
shock,  was  felt,  and  a  report  heard  like  that  of  a  heavy  body  falling 
to  the*ea'?lh  ;  but  no  conception  being  entertained  of  the  real  cause,  it 
was  supposed  that  lightning  had  struck  the  ground.  Three  or  four 
hours  after  this  event,  Mr.  Seely  went  into  his  field  to  look  after  his 
cattle.  He  found  that  some  of  them  had  leaped  into  the  adjoining 
enclosure,  and  all  exhibited  strong  indications  of  terror.  Passing  on 
he  was  struck  with  surprise  at  seeing  a  spot  of  ground,  which  lie 
knew  to  have  been  recently  turfed  over,  all  torn  up,  and  tlje  earth 
looking  fresh,  as  if  from  recent  violence.  Coming  to  the  plact;,  he 
found  a  great  mass  of  fragments  of  a  strange  looking  stone,  and  im- 
mediately called  his  wife,  who  was  second  on  the  ground. 

'•  Here  were  exhibited  the  most  striking  proofs  of  violent  collisicn. 
A  ridge  of  micaceous  schistus  lying  nearly  even  with  the  ground, 
and  somewhat  inclining  like  the  hill  to  tlie  south-east,  was  shivered 
to  pieces,  to  a  certain  extent,  by  the  impulses  of  the  stone,  whicn 
thus  received  a  still  more  oblique  direction,  and  forced  itself  into  the 
earth  to  the  depth  of  three  feet,  tearing  a  hole  of  five  feet  in  length, 
and  four  and  a  half  in  breadth,  and  throwing  large  masses  of  turf, 
and  fragments  of  stone  and  earth,  to  the  distance  of  50  and  100  feet 
Plad  there  been  no  meteor,  no  explosions,  and  no  witnesses  of  the 
light  and  shock,  it  would  have  been  impossible  for  any  person  con- 
templating the  scene  to  doubt  that  a  large  and  heavy  body  had  real- 
ly fallen  from  the  skies  with  tremendous  momc  ntuni. 

"  This  stone  was  all  in  fragments,  none  of  which  exceeded  the 
size  of  a  man's  fist,  and  was  rapidly  dispersed  by  numerous  visitors 
who  carried  it  away  at  pleasure.  Indeed  it  was  very  difiicult  to  ob- 
tain a  supply  of  specimens  of  the  various  stones,  an  object  v  Inch 
was  at  length  accomplished  principally  by  importunity  and  purchase. 
From  the  best  information  which  could  be  obtained  of  the  quantity 
of  fragments  of  this  last  stone,  compared  with  its  specific  gravity,  it 


Of  the  different  Systems.  115 

was  concluded  that  its  weight  could  not  have  fallen  much  short  of 
200  pounds.  All  the  stones  when  first  found,  were  friable,  bein^ 
easily  broken  between  the  finders ;  this  was  especially  the  case 
where  they  had  been  buried  in  the  moist  earth,  but  by  exposure  to 
the  air  they  gradually  hardened.  Sucii  were  the  circumstances  at- 
tending the  fall  of  these  singular  masses. 

"  The  specimens  obtained  from  all  the  diiTerent  places  are  per- 
fectly similar.  The  most  careless  observer  would  instantly  pro- 
nounce them  portions  of  a  common  mass,  and  different  from  any  of 
the  stones  commonly  seen  on  this  globe.'' 


Sect.  IT. 

Of  the  different  Sijstems, 

208.  The  systems  which  were  generally  received 
among  the  ancients  were  very  errgnedus.  (Et^omy^ 
who  has  given  Iiis  name  to  the  earliest  known  system, 
supposed  the  earth  to  be  at  rest  in  the  centre  of  the 
universe,  and  all  the  other  heavenly  bodies  to  revolve 
round  the  earth  in  the  follovv'ing  ordor;  viz.  the  Moon, 
ISIercur-y,  Venus,  the   Sun,  Mars,  Jupiter,  and  Saturn. 

^But  this  system  will  not  account  for  tlie  different  ap- 
pearances or  phases  of  Mercury  and  Venus,  and  con- 
sequently cannot  be  true. 

209.  This  system  was  soon  qualified  in  some  degree 
among  the  Egyptians.  :They  observed  that  Mercury 
and  Venus  w^ere  never  at  a  great  distance  from  tlie  sur/; 
whereas,  if  they  revolved  round  the  earth,  as  they  sup- 
posed the  sun  itself  did,  they  vvould  sometimes  be  \n 
opposition  to  the  sun,  as  the  other  planets  are.  Hencr^ 
they  w^ere  led  to  suppose  that  Mercury  and  Venur> 
moved  round  the  sun,  as  secondary  planets  move  round 
their  primaries,  and  were  at  the  same  time  carried  witr- 
tlie  sun  round  the  earth.  This  theory  accounts  for  all 
the  phases  of  Venus  and  Mercury  ;/but  it  will  not  ac- 
count for  the  different  (direct  and  retrograde)  motions 
of  the  exterior  planets. 


116  Of  the  different  Systems. 

210.  Of  the  ancients,  however,  the  Babylonians,  and 
afterwards  Pythagoras,  (about  500  years  before  the 
Christian  era,)  are  said  to  have  considered  the  earth  a 
planet,  revolving  round  the  sun,  like  the  other  planets. 
Though  we  can  hardly  conceive  how  the  truth  should 
have  been  lost,  when  once  discovered  and  promulgated, 
yet  this  knowledge  of  the  true  solar  system  was  very  soon 
lost ;  and  was  not  revived  till  about  the  middle  of  the 
sixteenth  century.  Copernicus,  from  whom  the  true 
system  is  called  Copernican,  supposed  the  earth  to  turn 
on  its  axis  every  day,  and  revolve  round  the  sun  every 
year.  These  two  motions  explain,  v.  ith  the  utmost  fa- 
cility, all  the  phenomena  of  the  stations,  motions,  and 
phases  of  all  the  other  heavenly  bodies ;  whence  arises 
the  'strongest  possible  proof  of  the  correctness  of  his 
supposition,  and  confirms  beyond  a  doubt  the  truth  of 
his  system.  For  nothing  can  be  consistent  with  itself 
but  truth. 

211.  Notwithstanding  the  siivplicity  of  tKJ*?  *heory, 
Copernicus  found  in  his  time  an  able  astronomer,  who 
rejected  the  evidences  of  the  truth  of  his  discovery. 
Tycho  Brahe,  a  Danish  nobleman,  was  anxious  to  re- 
concile the  appearances  of  nature,  v/ith  the  literal  inter- 
pretation of  some  passages  of  scripture.  He  therefore 
supposed  the  earth  immoveable  in  the  centre  of  the  or- 
bits of  the  sun  and  moon,  without  any  rotation  on  its 
axis  ;  but  he  made  the  sun  the  centre  of  tlie  orbits  of 
all  the  other  planets,  which  therefore  revolved  with  the 
sun  al^out  the  earth.  This  system  is  called  the  Tycho- 
nic.  The  principal  objection  to  it  is  its  want  of  sim- 
plicity;  also  the  necessity  of  supposing  that  all  the  hea- 
venly bodies  move  round  the  earth  every  day.  Some 
of  the  followers  of  Tycho  gave  a  rotatory  motion  to 
the  earth,  and  this  was  called  the  Senii-Tychonic  sys- 
tem. 4 But  the  Copernican  system  has  now  superseded 
all  others  throuorhout  Christendom. 


Sect.   III. 
Of  Leap   Year, 

212.  The  solar  year,  or  the  time  of  the  sun's  passing 
from  arr  equinox  to  his  return  to  the  same  again,  con- 
sists of(365  days,  5  hours,  48  minutes,  and  57  seconds. 
Hence  it  is  plain,  that  if  we  reckon  only  365  days  to  a 
civil  or  common  year,  the  sun  would  be  in  an  equinox, 
say  the  vernal,  later  in  every  succeeding  year,  than  in 
the  preceding,  by  5  hours,  48  minutes,  and  57  seconds ; 
that  is,  nearly  a  quarter  of  a  mean  day.  So  that  if  the 
sun  entered  Aries  on  the  20  March  one  year,  \\%  would 
enter  it  on  the  21  four  years  after,  and  on  the  22  eight 
years  after,  and  so  on.  Thus  in  a  comparatively  short 
time,  the  spring  months  would  come  in  the  winter  season, 
and  the  summer  months  in  the  spring  season. 

213.  To  prevent  the  confusion,  Vvhich  w^ould  result 
from  this  reckoning,  in  every  fourth  year,  generally^  a 
day  is  added  to  February,  viz.  in  such  years  as  may 
be  divided  by  4  w^ithout  a  remainder^  ''Such  years  are 
called  Bissextile^  or  Leap  years.  But^his  is  plainly 
allowing  too  much ;'  for  the  excess  over  365  days  is  not 
equal  to  a  quarter  of  a  day,  by  1 1  minutes,  3  seconds. 
This  would  amount  to  a  wiiole  day  in  about  130  years. 
To  prevent  the  error,  v/hich  would  thus  result|.it  was 
settled  by  an  act  of  parhament,  that  the  years  1800  and 
1900,  (though  divisible  by  4,)  should  not  be  leap  years. 
And  afterwards  the  closing  year  of  only  every  fourth 
century  should  be  a  leap  year.  If  this  method  be 
adhered  to,  the  present  mode  of  reckoning  will  not  vary 
a  single  day  from  true  time,  in  less  than  5000  ye^s 

11* 


tl8  Of  Cycles. 

Sect.  IV. 
Of  Old  and  JVew  Style. 

214.  Among  different  ancient  nations,  different  meth- 
ods of  computing  the  year  were  in  use.  ^ome  deter- 
mined it  by  the  revohitions  of  the  moon  ;  some  by  that 
of  the  sun.  But  none  (so  far  as  we  know)  made  prop- 
er allowance  for  deOciencies  and  excesses.  Twelve 
moons  fell  short  of  the  true  year  ;  13  exceeded  it ;  365 
days  were  not  enough  :  36(3  were  too  many.  To  pre- 
vent the  confusion  resultins;  from  these  erroneous  esti- 
mates, ♦Julius  Caesan  reformed  the  calendar, 'by  making 
the  year  consist  of  365  days,  6  hours,  (which  is  hence 
called  di^ Julian  year,^  and  made  every  foui^th  year  con- 
sist of  366  days.     This  method  of  reckoning  is  called 

fold  Style] 

215.  But  as  this  made  the  year  somewhat  too  long, 
pope  .Gregory  XIII.,  in  order  to  bring  the  vernal  equinox 
on  the  ^1  March,  ordered  10  days  to  be  struck  out  of 
the  year  1582  ;  calhng  the  next  day  after  the  4th  Octo- 
oer,  the  15th.  (And  by  omitting  3  intercalary  days  in 
400  years,  he  intended  that  the  civil  and  solar  year 
should  keep  together.  This  form  of  the  year  is  called 
the  Gregorian  Account,  or  J\^eiv  Style.  Though  this  al- 
teration was  immediately  adopted  throughout  the  greatest 
part  of  Europe,  it  was  not  admitted  by  the  Enghsh  till 
the  year  17524  Th-^  error  at  that  time  amounted  to 
nearly  1 1  days,  w^hich  were  taken  from  the  month  of 
September,  by  calling  the  3d  of  that  month  the  14th. 

Sect.  V. 

Of  Cycles. 

216.  Under  the  Art.  EcLiPSES^^t  was  stated  that  the 
line  of  the  moon's  nodes  went  backwards,  completing  a 


Of  Cycles.  119 

revolution  in  little  less  than  19  years.^  This  period  is 
the  Cyde  of  the  Moon,  usually  called  the  Golden  JVum-- 
ber.  r'The  conjunctions,  oppositions,  and  other  aspects 
of  the  moon  are  within  an  hour  and  a  half  of  being  the 
same  as  they  were  on  the  same  days  of  the  month  19 
years  before/  Consequently,  very  nearly  the  same  order 
of  echpses  occur  every  nineteenth  year.  To  find  the 
Golden  JVumber  for  any  year^  add  1  to  that  year,  divide 
the  number  by  19,  and  the  remainder  is  the  Golden 
Number.  If  nothing  remains,  the  Golden  Number 
is  19. 

217.  The  Cycle  of  the  Sun  is  a  revolution  of  28 
years  ;  in  which  time  the  days  of  the  months  return 
again  to  the  same  days  of  the  week  ;  the  sun's  place  to 
the  same  signs  and  degrees  of  the  Ecliptic  on  the  same 
months  and  days,  so  as  not  to  differ  a  degree  in  100 
years ;  and  the  leap  years  begin  the  same  course  over 
again,  with  respect  to  the  days  of  the  week,  on  which 
the  days  of  the  monlhs  fall.  To  find  the  Cycle  of  the 
Sun,  add  9  to  the  given  year,  divide  by  28,  and  the  re- 
mainder is  the  Cycle  of  the  Sun,  for  that  year.  If 
nothing  remains,  the  Cycle  is  28. 

218.  In  the  subjoined  table,  the  Golden  Numbers 
under  the  months  stand  against  the  days  of  new  moon, 
in  the  left  hand  column.  It  is  adapted  chiefly  to  the 
second  year  after  leap  year,  and  will  indicate  the  time 
of  new  moon,  (within  1  day,)  till  the  year  1900.  A 
perfectly  correct  table  of  this  kind  cannot  be  easily  con- 
structed. 

To  show  the  use  of  this  Table,  suppose  I  want  to 
know  nearly  the  time  of  the  new  moon  in  Oct.  1822. 
By  the  above  Rule,  I  find  the  Golden  JVumber  for  this 
year  to  be  18.  Under  the  month  Oct.  in  the  Table,  I 
find  the  Golden  JVumber  18  placed  against  the  14th  day 
in  the  left  hand  column  ;  that  is,  it  is  new  moon  on  the 
Hth  day,  or  near  it.     The  error  cannot  exceed  1  day. 


120 


Of  Cycles. 


9 

• 

3 

Feb. 

j 

s 

i 

O 

o 

o 
< 

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9 

R 

1717 

i 

11 

il9 

2 

17 

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6 

14 

14  3!n 

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8 

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4 

6 

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!.]• 

8 

11 

19 

8 

8 

16 

5 

5 

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9 

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19 

11 

19 

13 

2 

10 

19 

8 

8 

16 

16 

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16 

8 

16 

\6 

5 

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13 

5 

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10 

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7 

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5 

16 

5 

210 

18 

18 

7 

15 

5 

5 

13 

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2 

i 

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10 

lOilS 

7 

15 

17 

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19 

Of  the  Dominical  Letter.  121 

Sect.  VI. 
Of  the  Doininical  Letter, 

219.  The  Dominical  Letter  for  any  year  is  that 
which  is  placed  against  Sunday  in  common  almanacks  ; 
and  is  always  one  of  the  seven  first  of  the  alphabet. 
Since  a  common  Julian  year  consists  of  365  days,  if 
this  number  be  divided  by  7,  (the  number  of  days  in  a 
week,)  there  will  be  1  remainder.  Hence  it  is  obvious, 
that  commonly  a  year  begins  one  day  later  in  the  week, 
than  the  preceding  one  did.  Thus,  if  a  year  of  365 
days  begins  on  Sunday,  the  following  year  will  begin  on 
Monday.  If  Sunday  fahs  on  \he  first  day  of  January, 
the  first  letter  of  the  alphabet  (A)  is  the  Dominical 
Letter.  If  Sunday  falls  on  the  seventh  day  of  January, 
(as  it  will  in  the  2d  year,  unless  the  1st  be  leap  year,) 
then  ihe  seventh  letter  of  the  alphabet  (G)  is  the  Do- 
minical Letter.  If  Sunday  falls  on  the  sixth  day  of 
January,  (as  in  the  3d  year,  unless  the  1st  or  2d  be 
leap  year,)  the  sixth  letter  of  the  alphabet  (F)  is  the 
Dominical  Letter.  Hence  it  is  plain,  that  if  there  were 
no  leap  years,  the  Dominical  Letters  would  go  annually 
;n  a  retrograde  order,  thus,  G,  F,  E,  D,  C,  B,  A. 

220.  /^But  Leap  years  have  366  days  ;  which,  divided 
by  7,  leaves  2  remainder.  Hence,  the  years  following 
leap  years  will  begin  2  days  later  in  the  week,  than  the 
leap  years  did.  Thus,  if  a  leap  year  begins  on  Monday, 
(the  Dominical  Letter  being  G,)  the  following  year  will 
begin  on  Wednesday,  and  the  Dominical  Letter  will  be 
K,  F  being  passed  over.  To  prevent  the  interruption, 
which  would  thus  occur  in  the  order  of  the  Dominical 
Letters,  leap  years  have  2  Dominical  Letters ;  one  in- 
dicates Sunday  till  the  24th  of  February,  and  the  other 
till  the  end  of  the  year. 


122  Of  the  Dominical  Letter. 

221.  By  Table  L  at  the  close  of  this  Sect,  the  Do- 
minical Letter  for  any  year,  (New  Style,)  within  4,000 
years  following  the  Christian  asra,  can  be  readily  found. 
Look  for  the  hundreds  of  years  at  the  head  of  the  col- 
umn^ and  for  the  years  below  a  hundred  {to  make  up  the 
given  year)  at  the  left  hand.  Thus,  if  I  want  to  know 
the  Dominical  Letter  for  1822,  I  look  for  the  column 
containing  1800  at  the  top  ;  and  in  that  column,  oppo- 
site 22  in  the  left  hand  column,  I  find  the  Dominical 
Letter  of  that  year,  viz.  F.  Again,  if  I  want  to  know 
the  Dominical  Letter  for  1940,  I  find  the  column  con- 
taining 1900  at  top,  and  in  that  column,  against  40  in  the 
left  hand  column,  are  G  and  F,  which  are  the  Domini- 
cal Letters  for  that  year.  Because  there  are  2  letters 
against  that  year,  I  know  it  is  a  leap  year. 

222.  Having  the  Dominical  Letter  for  any  year. 
Table  IL  shows  what  days  of  every  month  in  the  year 
will  be  Sundays;  whence  may  be  readily  seen  Vvhat 
day  of  the  week  falls  upon  any  given  day  in  the  year. 
For  under  the  Dominical  Letter  at  the  top  are  the 
Sundays  of  that  year  ;  and  next  to  the  Sundays,  on  the 
right,  are  the  Mondays,  and  next  are  the  Tuesdays,  and 
so  on  to  the  last  column  ;  from  which  go  to  the  left 
hand  column,  and  proceed  as  before  to  the  right  hand. 
Thus,  if  I  want  to  know  wtiat  day  of  the  week  falls  on 
the  1st  of  Sept,  1822,  1  find  the  Dominical  Letter  of 
that  year  to  be  F,  and  undei-  F,  against  the  Month  Sept. 
I  find  the  1st  day.  Hence  the  1st  day  is  Sunday,  the 
2d  Monday,  and  so  on.  Again,  to  know  what  day  of 
the  week  will  fall  on  the  15th  day  of  July,  1831,  by 
Table  L  I  find  the  Dominical  liCtter  of  that  year  is  B; 
in  Table  II.  under  B,  and  against  July,  I  find  that 
Sunday  falls  on  the  10th,  consequently  the  15th  will  be 
Friday. 

Let  ihe  pupil  be  exercised  in  solving  questions  by  these  Tables 
\\\)  their  application  becomes  easy. 


Of 


Donuncal  Letter. 


VI: 


■ii 


pa 


d 


*s^ 


O 
O 

c 


^ 


CO 


Q     - 


^ 


CO 


Alter  Chr.iHundred 

s  oi*  ) 

'ears. 

100;  200   300,  400 

5001  600    700    800 

OOO'lOOO  I100!l200 

1300:i400ll500|l600 

Years    less 

1700:i800  1900'2i)00 

than  a 

2190  220012300  2400 

hundred 

2500  2600!2700|2800 

2900i3000i3lOC 

3200 

3300i340( 

)  35O0 

3600 

3701 
C 

380r 
E 

)390C 
G 

4000 

B  A 

]  29  57  85 

B 

D 

F 

G 

230  58  86 

A 

C 

E 

E 

^ 

31  59  87 

G 

B 

D 

F 

4 

32,60^88 

F  E 

AG 

C  B 

D  C 

5 

33|'0l|89 

D 

F 

A 

B 

6 

34  02' 90 

C 

E 

G 

A 

7 

35  03^91 

B 

D 

F 

G 

8 

30/J4j92 

A  GjC  B 

E  D 

F  E 

(j 

37:G5|93 

r 

A 

C 

D 

10 

38^)6 

94 

E 

G 

B 

C 

Jl 

159  07 

95 

D 

1' 

A 

B 

i;2 

40  68 

90 

C  B 

E  D 

G  F 

A  G 

13 

A^  09 

97 

A 

C 

E 

F 

14 

42  70 

98 

G 

B 

D 

E 

15 

43  71 

99 

F 

A 

C 

D 

10 

1 

44  72 

E  D 

G  F 

B  A 

C  B 

17 

45  73 

C 

E 

G 

A 

18 

40 

74 

B 

D 

F 

G 

19 

47 

75 

A 

C 

E 

F 

20 
21 

48 
49 

70 

G  F 

B  A 

D  C 

E  D 

77 

E 

G 

B 

C 

22 

50  78 

D 

F 

A 

B 

23 

51  79 

C 

E 

G 

A 

24 

52  80 

B  A 

D  C 

F   E 

G  F 

25 

5381 

G 

B 

D 

E 

26 

54182 

F 

A 

C 

D 

27 

55183 

E 

G 

B 

C 

28 

56184 

D  C 

F  E 

AG 

A  b! 

124 


Of  the  Dominical  Letters. 

Week  days. 

A 

B 

C 

D 

E 

F 

G 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

d 

V 

January  31 
October  31 

15 

22 

16 
23 

17 

24 

18 
25 

19 
2^ 

20 

27 

21 
28 

50 

29 

30 

31 

— 

— 

"""" 

1 
8 

2 
9 

3 
10 

4 
11 

5 

6 

7 

s 

Feb.  28-29 

12 

13 

14 

15 

16 

17 

18l 

1 

March  31 

19 

20 

21 

22 

23 

24 

25 

;5> 

November  30 

26 

27 

28 

29 

30 

31 

1 
8 

2 

3 

4 

5 

6 

7 

-^ 

9 

10 

11 

12 

13 

14 

15 

April  30 

16 

17 

18 

19 

20 

21 

22' 

5^ 

July  31 

23 
30 

24 
31 

25 

26 

27 
— 

28 

29: 

1 

4 

1 

8 

15 

2 

9 

16 

3 
10 
17 

4 
11 
18 

5i 
12| 
191 

6 
13 

7 
14 

Eh 

oT 

August  31 

20 

21 

22 

23 

24 

25 

26^ 

27 

28 

29 

30 

31 

— 

! 

1 

1 
8 

Oi 

3 

4 

5 

6 

7 

9i 

»< 

10 

11 

12 

13 

14 

\5 

16| 

V 

September  30 

17 

18 

19 

20 

21 

22 

23i 

Co 

December  31 

24 

25 

26 

27 

28 

29 

30i 

# 

31 

— 

— 

— 

— 

— 

— 

1 

2    3 
9jlO 

4     ^1 

6 
13 

7 

1 

8 

'1- 
11 

12 

14 

15 

16 

17 

18 

19 

20 

1 

May  31 

21 
28 

22 
29 

23 
30 

24 
31 

25 
1 

26 
2 

27 
3 

4 

5 

6 

7 

1 

8 

9 

10 

11 

12 

13 

14 

15^16 

17 

June  30 

18 

19 

20 

21 

22  23 

24 

25 

56 

27 

28 

29  30 

125 
Sect.  Vll. 

Of  Epact. 

223.  A  Julian  year  consists  of  365  days,  6  hours, 
and  a  lunar  year,  of  12  moons,  consists  of  354  days,  8 
hours,  49  minutes.  This  difference  of  nearly  11  days 
between  a  solar  and  a  lunar  year  is  the  Annual  Epact. 
Since  the  epact  of  one  year  is  1 1  days,  the  epact  of  two 
years  is  22  days,  of  three  years  is  33  days,  or  rather  3 
days )  being  3  days  over  a  complete  limation.  Hence 
the  epact  of  four  years  is  14  days.  Thus  by  yearly 
adding  11,  and  casting  out  the  30s  for  intercalary  luna- 
tions, (for  when  30  is  cast  out,  the  lunar  year  must  con- 
sist of  13  lunations,)  it  will  be  found,  that  on  every  19th 
year  29  remains  ;  which  is  reckoned  a  complete  luna- 
tion, and  the  epact  is  0.  Thus  the  cycle,  or  succession 
of  epacts,  expires  with  the  Golden  Number,  or  lunar 
cycles;  and  on  every  19th  year  the  solar  and  lunar 
year  begin  together.  By  the  epact  of  any  year,  the 
moon's  age,  or  the  number  of  days  since  her  change, 
is  at  once  seen,  for  the  first  day  of  January.  In  the 
following  Table  is  exhibited  the  Golden  Numbers,  with 
the  corresponding  epacts,  till  the  year  1900  of  the 
Christian  a?ra. 

TABLE. 


Cjiolden 
number 

Epact. 

Golden 
number 

Epact. 

Golden 
number 

Epact. 

Golden 
number 

Epact. 

1 

3 
t 

5 

XI. 
XXII. 

III. 

XIV. 

6 
7 
8 
9 
10 

XXV. 

VI. 

XVII. 

XXVIII. 

IX. 

11 
12 
13 
14 
15 

XX. 

I. 

XII. 

XXIII. 

IV. 

16 
17 
18 
19 

XV. 
XXVI. 

VII. 
XVIII. 

224.  The  Indiction  is  a  revolution  of  15  years,  used 

only  by  the  Komans  for  indicating  the  times  of  certain 
^12 


1 26  Problems, 

payments  made  by  the  subjects  to  the  Republic.  Bv 
the  multiphcation  of  the  Cycle  of  the  Sun  (28  years) 
into  the  Cycle  of  the  Moon  (19  years)  and  the  Indlction 
(15  years)  arises  the  Great  Julian  Period^  consisting  of 
7980  years. 

Sect.  VIIL 

problems. 

A  few  of  the  most  useful  and  interesting  ProhJems  are 
here  inserted,  for  such  pupils  as  have  globes  at  hand, 
and  instructers,  who  can  point  out  and  explain  the  use 
of  the  different  circles  and  appurtenances  belonging  to 
them. 

Art.  1. 
ProhJems  to  be  solved  by  the  Terrestrial  Globe. 

225.  Prob.  1. — To  find  the  latitude  of  any  given 
place. 

Bring  the  place  to  the  graduated  side  of  the  brazen 
meridian,  and  the  degree  of  the  meridian  over  the  place 
is  the  latitude. 

1.  What  is  the  latitude  of  Boston  ?     Ans.  42^  28'  N 

2.  Find  the  latitude  of 

Amsterdam,  Constantinople,        Quebec, 

Aleppo,  Florence,                  Rome, 

Alexandria,  Cape  Farewell,       Stockholm, 

Athens,  C.  of  Good  Hope,  Savannah, 

Bourbon  isl.  Lima,                        Tripoli, 

Bayonne,  New  Orleans,          Upsal, 

Barbadoes  isl.  Naples,                     Vienna, 

Canton,  Panama,                   Warsaw, 

Cairo,  Paris,                        Washington. 

226.  Prob.  II. — To  find  the  longitude  of  a  given 
place. 

Bring  the  place  to  the  brazen  meridian,  and  the  de 
^ree  of  the  equator  under  the  meridian  is  the  longitude 


Problems.  127 

1.  What  is  the  longitude  of  Petersburg?  Ans.  30° 
15'  E. 

2.  What  is  the  longitude  of  Philadelphia  ?  Ans.  75° 
15'  W. 

3.  Find  the  longitude  of  the  places  mentioned  in  the 
preceding  number. 

227.  Prob.  hi. —  To  find  the  difference  of  latitude 
betiveen  any  two  places. 

Find  tb.e  latitude  of  each  place,  by  Prob.  I.  If  both 
are  north,  or  both  south  latitude,  subtract  the  less  from 
the  greater  ;  but  if  one  be  north  and  the  other  south, 
add  them  together,  and  the  resu'lt  will  be  the  answer. 

1.  What  is  the  difference  of  lathude  between  Peters- 
burg and  Philadelphia  ?     Ans.  20°. 

2.  What  is  the  difference  of  latitude  between  Boston 
and  Cape  Horn  ?     Ans.  97°  30\ 

3.  Required  the  difference  of  latitude  between 
London  and  Rome,  Panama  and  V^alparaiso, 
Madrid  and  Moscow,         Boston  and  Montreal, 
Quebec  and  N.  Orleans,  Edinburgh  and  Baltimore, 
Pekin  and  Lisbon,             Cape  Cod  and  Cape  Henry, 
Calcutta  and  Delhi,            Hahfax  and  Canary  Islands, 
Hague  and  Lima,               Gibraltar  h  Cape  of  G.  Hope. 

228.  Prob.  IV. —  To  find  the  difference  of  longitude 
between  any  two  places. 

Find  the  longitude  of  each  place  by  Prob.  II.  If  both 
be  in  east,  or  both  in  west  longitude,  subtract  the  less 
from  the  greater,  and  the  result  is  the  answer.  But  if 
one  be  east  and  the  other  west,  add  them  together,  and 
if  the  sum  be  less  than  180°,  it  is  the  answer;  but  if 
more,  take  it  from  360°,  and  the  remainder  is  the 
answer. 

Find  the  difference  of  longitude  between  the  places 
mentioned  in  the  preceding  number. 


128  Problems. 

229.  Pkob.  V. —  To  find  the  distance  in  miles  between 
any  two  jjlaces  on  the  s^lohe. 

Lay  the  quadrant  of  altitude  over  both  places,  and  it 
will  show  the  number  of  degrees,  which  multiply  by 
no^,  and  it  will  give  the  distance  in  miles. 

J .  What  is  tlie  distance  between  Londoii  and  Jamaica.'* 
Ans.  671^  or  4691  miles. 

2.  What  is  the  distance  between 
Cadiz  and  Petersburg,  Washington  and  Madrid, 

Cape  Horn  and  Good  Hope,  Philadelphia  and  Venice, 
New  York  and  London,        Cuba  and  Cyprus, 
Charleston  and  Fez,  London  and  Bombay  ^ 

230.  Prob.  VL — The  hour  of  the  day  at  any  place 
being  given,  to  find  what  o'clock  it  is  at  any  other  place. 

Bring  the  place,  where  the  hour  is  given,  to  the  brazen 
meridian  :  set  the  index  to  the  given  hour,  then  turn  the 
globe  till  the  proposed  place  comes  under  the  meridian; 
the  index  will  point  to  the  hour  required. 

J\'ote.     If  the  place  required  be  east  of  the  given  place,  turn  the 
globe  westward ;  if  to  the  west,  turn  the  globe  eastward. 

1.  Wlien  it  is  12  o'clock  at  noon,  in  London,  what  is 
the  time  at  Mauritius  and  Philadelphia  ? 

Ans. — Four  P.  M.  at  ^Mauritius,  and  7  A.  M.  at 
Philadelphia. 

2.  When  it  is  8  o'clock  A.  M.  at  Boston,  what  is  the 
time  at  Acapulco  and  Cape  Farewell  ? 

Ans. — 6  A.  M.  at  Acapulco,  and  10  A.  M.  at  Cape 
Farewell. 

3.  When  it  is  midnight  at  Boston,  what  o'clock  is  it  at 
Paris,  Canton,  New  Orleans, 
Rome,                      Calcutta,  Rio  Janeiro, 
Petersburg,             Cairo,                       Ascension  Island  ? 

4.  When  it  is  noon  at  Lisbon,  what  is  the  hour  at 
Quebec,  Cape  Horn,  Jerusalem, 
Mexico,                   Berm.idas,  Cape  Comorin, 


Probcerrid.  129 

Pekin,  St.  Helena,  Athens, 

Babelmande.,         Botany  Bay,  Tripoli  ? 

231.  Prob.  VII. — The  hour  of  the  day  being  given 
at  any  place ^  to  find  all  the  places  on  the  globe  where  it 
is  any  other  given  hour. 

Bring  the  place  to  the  brazen  meridian,  and  set  the 
index  to  the  hour  of  that  place  ;  turn  the  globe  till  the 
index  points  to  the  other  given  hour,  then  all  the  places 
under  the  meridian  are  the  places  required. 

1.  When  it  is  12  at  noon,  in  London,  at  what  places 
is  it  8  A.  M.  ? 

Ans. — Cape  Canso,  Martinico,  Trinidad,  fcc. 

2.  When  it  is  2  P.  M,  in  London,  where  is  it  half 
past  5  P.  At  ? 

Ans. — Caspian  Sea,  Socotra,  Madagascar,  &c. 

3.  When  it  is  5  A.  M.  at  Madrid,  where  is  it  noon  ? 

4.  When  it  is  noon  at  New  York,  where  is  it  5  P.  M.  ? 

5.  When  it  is  10  A.  M.  at  New  York,  where  is  it  noon  ? 

6.  When  it  is  noon  at  Paris,  where  is  it  midnight  ? 

7.  Does  the  sun  rise  first  upon  Cape  Farewell  or 
New  Orleans  on  Ma^ch  21  ? 

8.  Does  the  sun  set  soonest  at  the  Bermuda  islands, 
or  in  the  gulf  of  Cahfornia  ?      How  much  ? 

9.  What  places  have  6  o'clock  A.  M.  when  it  is  noon 
at  the  Falkland  islands  ? 

10.  When  it  is  noon  at  Lisbon,  at  what  places  is  it  8 
o'clock  in  the  afternoon,  and  at  what  places  is  it  6  o'clock 
in  the  forenoon  ? 

232.  Prob.  VIII.— To^n^  the  antipo^mjfffahyp^acc 
Bring  the   given  place  to  the  meridiSti,  and  find-S 

latitude  ;  set  the  index  to  12,  and  turn  the  globe  till  the 
index  points  to  the  other  12  ;  then  the  same  degree  of 
latitude  on  the  other  side  of  the  equator  shows  the  an- 
tipodes, thus : 

1 .  What  is  the  antipodes  of  London  f 

Ans. — The  south  part  of  New  Zealand. 
12* 


130  Problems, 

2.  What  is  the  antipodes  of  the  Buirnudas.^ 
.\ns. — South  west  part  of  New  Holland. 

3.  What  is  the  antipodes  of  the  Society  Islands  ? 
/Vns.— The  Red  Sea. 

4.  What  is  the  antipodes  of 

Boston,  Caspian  Sea,  Spam, 

Terra  del  Fue^o,       Egypt,  Persia? 

233.  Prob.  IX. —  To  find  at  ichat  rate  per  hour  the 
tnhabitants  of  any  given  place  are  carried  by  the  revolu- 
lion  of  the  earth  on  its  axis. 

Find  how  many  miles  make  a  degree  of  longitude  in 
the  latitude  of  the  given  place,  (see  Table,  page  45.) 
which  muhiply  by  15  for  the  answer. 

At  what  rate  per  hour  are  the  inhabitants  of  the  fol- 
lowing places  carried  by  the  motion  of  the  earth  on  its 
axis  ? 

Petersburg,  Cape  of  Good  Hope, 

London,  Calcutta, 

Boston,  De]'- 

Quito,  Batavia  f 

234.  Prob.  X. —  The  day  of  the  month  being  given, 
to  find  the  si^^s  place  or  longitude  in  the  ecliptic,  and  its 

declination. 

Look  for  the  given  day  in  the  circle  of  months  on  the 
horizon,  and  opposite  to  it  in  the  circle  of  signs,  are  the 
sign  and  degree  the  sun  is  in  on  that  day.  Find  the 
same  sign  and  degree  in  the  ecliptic,  and  it  will  be  the 

[*s  place' or  longitude  :  brii\g  this  place  to  the  merid- 

,  and  you  will  have  the  declination. 

1 .  What  is  the  sun's  longitude  and  declination  on  the 
22  of  February: 

Ans. — 337*" '30'  or  4°  30'  in  Pisces;  its  declination 
is  10°  south. 

2.  What  is  the  sun's  longitude  and  declination  on  tbo 
15  of  April.? 


Problems,  131 

Ans. — 25*^  30',  in  Aries;  its  declination  10®  north. 

3.  When  does  the  sun  enter  each  of  the  signs  ? 

4.  What  is  the  sun's  dechnation  on  the  21  of  June  .'' 

5.  What  is  the  sun's  place  and  declination  on  the  22 
of  December  ? 

6.  What  is  the  sun's  place  in  the  ecliptic,  and  its  dec- 
lination, on  each  of  the  following  days  : 

March  30  July  13  November     2 

April       4  August  8  December  29 

May       12  September  16  January  7 

June        9  October  5  February     18 

235.  Prob.  XI. —  To  rectify  the  globe  for  the  lati" 
iude,  zenith^  and  sunh  place  on  any  day. 

1.  For  the  Latitude.  Elevate  the  pole  till  the 
horizon  cuts  the  brass  mer  Man  in  the  degree  corres- 
ponding to  the  latitude  of  the  place. 

2.  The  given  place  is  then  in  the  zenith. 

3.  Then  (by  Problem  X.)  find  the  sun's  place  foi* 
the  given  day,  brmg  it  to  the  meridian,  and  set  the  in- 
dex to  12. 

Xote.  If  the  place  be  in  north  latitude,  elevato  the  north  pole,  if 
in  south  latitude,  elevate  the  south  pole. 

1.  Rectify  the  globe  for  the  latitude  of  London,  on 
the  10  of  May. 

In  this  case  elevate  the  north  pole  51°  30',  then  Lon- 
don will  be  in  the  zenith,  over  it  screw  the  quadrant  of 
altitude  ;  the  10  of  May  on  the  horizon  answers  to  the 
twentieth  degree  of  Taurus,  which  find  on  the  ecliptic, 
and  bring  it  to  the  meridian,  and  set  the  index  to  12. 
This  is  the  position  of  the  globe,  as  it  appears  to  the 
inhabitants  on  the  10  of  May. 

2.  Rectify  the  globe  for 

New  York  12  January,  Madrid  ]  6  Sept. 

Boston  6  Feb.  Cape  Horn        15  Nov. 

Constantinople    9  March,  St.  Jago(Chih)  14  Dec. 

Petersburg        10  April,  GaUipagos  19  Oct. 


132  Problems, 

236.  Prob.  XII. — The  month  and  day  of  the  month 
Oeing  given,  to  find  all  those  places  on  the  globe,  which 
will  have  a  vertical  sun  on  that  day. 

Find  the  sun's  place  in  the  ediptic  (Prob.  X.)  and 
bring  it  to  the  meridian  ;  turn  the  globe  round,  and  all 
the  places  that  pass  under  that  degree  of  the  meridian 
will  have  a  vertical  sun  on  that  day. 

1.  Find  all  the  places  which  have  a  vertical  sun  on 
the  22  of  February. 

Ans. — Peru,  Amazonia,  Angola,  New  Guinea,  Queen 
Charlotte's  Island,  he, 

2.  What  places  have  a  vertical  sun  on  the  9  of  May  ^ 

3.  What  places  will  have  a  vertical  sun  on  the 

21  of  March,  23  of  Sept. 

21  of  June,  22  of  Dec. .? 

237.  Prob.  XIII. — To  fi  id  at  what  hoin^  the  sun 
rises  and  sets  at  any  place,  any  day  in  the  year,  and  the 
length  of  the  day  and  night  at  that  place, 

1.  Rectify  the  globe  (by  Prob.  XI.)  for  the  latitude 
of  the  place  ;  find  the  sun's  place  in  the  ecliptic  (by 
Prob.  X.)  and  bring  it  to  the  meridian,  and  set  the  in- 
dex to  12  ;  bring  the  sun's  place  to  t^e  eastern  edge  of 
the  horizon,  and  the  index  will  show  the  hour  of  rising ; 
bring  it  to  the  western  edge  of  the  horizon,  and  the  in- 
dex will  show  the  hour  of  setting. 

2.  Double  the  time  of  sun-rising,  and  it  will  give  the 
length  of  the  night ;  double  the  hour  of  sun-setting,  and 
It  will  give  the  length  of  the  day. 

1  What  time  does  the  sun  rise  and  set  at  New  York, 
on  the  10  of  May,  and  what  is  the  length  of  the  day  and 
night  f 

Ans. — It  rises  56  minutes  past  4  ;  sets  4  minutes  after 
7]  length  of  the  night  9h.  52m.;  of  the  day  14h.  8m. 

2.  What  is  the  time  of  sun-rising  and  sun-setting,  and 
the  length  of  the  day  and  night,  at  each  of  the  follow 
ing  places,  on  the  day  mentioned  ? 


Problems. 


\m 


Boston  7  Nov. 

Washington  city  4  May 
Constantinople    14  June, 
London  15  July, 

Rio  Janeiro  8  Sept. 


Cape  Horn  1  Dec. 

Rome  5  January, 

Naples  9  Oct. 

Canton  8  August. 


238.  Prob.  'KW ,—  To  find  the  length  of  the  longest 
and  shortest  days  and  nights  in  any  part  of  the  world, 

1.  If  the  place  be  in  the  northern  hemisphere,  rectify 
the  globe  for  the  latitude  of  the  place,  bring  the  first 
d(  gree  of  Cancer  to  the  meridian,  and  proceed  as  m 
the  last  problem. 

2.  If  the  place  be  in  the  southern  hemisphere,  bring 
the  first  degree  of  Capricorn  to  the  meridian,  and  pro- 
c<5ed  as  before. 

1 .  What  is  the  length  of  the  longest  day  and  shortest 
night  at  New  York  ? 

Ans. — Longest  day  14h.  56m.  shortest  night  9h.  4m. 

JVote.  The  shortest  night  of  any  place  is  equal  to  its  shortest  day, 
when  the  sun  is  on  the  other  side  of  the  equator,  and  its  longest  day 
to  its  longest  night. 

2.  What  is  the  length  of  the  longest  day  and  shortest 
night  at  each  of  the  following  places  ? 


Boston,  London, 

Philadelphia,  Iceland, 

Mexico,  Cape  Verd, 

Hahfax,  Suez, 

Quebec,  Bombay, 

Augusta,  Canton, 

New  Orleans,  Madagascar, 

Quito,  Abo, 

Chiloe,  Berlin, 

Their  shortest  day  and  longest  night  are  shown  by 
the  above  note 


River  Zaire, 

Botany  Bay, 

Madras, 

Mouth  of  Columbia 

river, 
Hudson's  Bay, 
Dardanelles, 
Azores, 
Isles  of  Georgia. 


134-  Problems, 

239.  Prob.  XV. — The  month  and  day  of  the  month 
being  given,  to  find  those  places  where  the  sun  does  no 
set,  and  lohere  it  does  not  rise  on  the  given  day. 

Find  the  sun's  declination  (by  Prob.  X.)  elevate  the 
pole  for  the  declination,  in  the  same  manner  as  for  the 
latitude  ;  turn  the  globe  on  its  axis,  and  on  the  places 
round  the  pole,  above  the  horizon,  the  sun  does  not  set ; 
and  on  the  places  round  the  other  pole,  below  the  hori- 
zon, the  sun  does  not  rise,  on  that  day. 

1.  How  much  of  the  south  frigid  zone  is  darkened, 
and  how  much  of  the  north  frigid  zone  is  enhghted, 
on  the  20  of  May  ? 

Ans. — 20°  round  each  pole. 

2.  On  which  pole  does  the  sun  rise  on  Nov.  6. 

3.  Which  frigid  zone,  and  how  much  of  it,  has  con- 
stant day,  on  August  4  ^ 

4.  How   much  of  the  south  frigid  zone  has  constant 
day  on  the  following  days  ^ 
October     1,  Dec. 
October  20,                     Jan. 
Nov.        19,  Feb. 

5.  What  days  in  the  year  does  the  sun  shine  equally 
on  both,  poles  ^ 

Art.  2. 
Problems  to  be  solved  by  the  celestial  globe. 

240.  Prob.  XVI. —  To  find  the  right  ascension  of  the 
sun  or  a  star. 

Bring  the  sun's  place  in  the  ecliptic  or  the  star  to  the 
brass  meridian,  then  the  degrees  of  the  equinoctial  un- 
der the  meridian,  reckoning  from  Aries  eastward,  is  the 
right  ascension, 

1.  What  is  the  sun's  right  ascension  on  the  19  of 
April .?     Ans.— 27°  30\ 

2.  What  is  the  sun's  right  ascension  on  the  1  Dec.  ? 
Ans.— 247°  50  . 


22, 

Feb.     20, 

9, 

March     1. 

10, 

Problems.  135 

3.  What  is  the  sun's  right  ascension  on 

Nov.      6,'  July      29,  Sept.  14, 

March   4,  May        7,  Oct.    23, 

April   20,  August  10,  Dec.    10? 

June    16, 

4.  What  is  the  right  ascension  of  Aldebaran  ? 
Ans.— 66°  6'. 

5.  W]iat  is  the  right  ascension  of 

Ahoth,  -  Fomalhaut,  Rigel, 

Arcturus,  Hyades,  Sirius, 

Bellatrix,  Pleiades,  Antares, 

Castor,  Procyon,  Pollux  ? 

Algol,  Regulus, 

241.  Prob.  XVII. —  To  find  the  declination  of  the 
sun  or  a  star. 

Bring  the  sun's  place  in  the  ecliptic  or  the  star  to  the 
brass  meridian,  and  the  degree  of  the  meridian  ove^ 
that  place  will  be  the  declination. 

1.  What  is  the  declination  of  the  sun,  April  19  ? 
Ans.— ir  19'. 

2.  What  is  the  sun's  declination, 

January      18,  March     2,  May    23, 

February  12,  April     12,  June    21? 

3.  What  is  the  declination  of  Aldebaran  ? 
Ans.— 16°  6^ 

4.  What  is  the  dechnatlon  of 

Atair,  Arcturus,  Regulus, 

Algenib,  Procyon,  Regel  ? 

242.  Prob.  XVIII. —  The  latitude  of  the  place,  the 
day  and  hour  being  given,  to  place  the  globe  so  as  to  rep- 
7'esent  the  appearance  of  the  heavens  at  that  time  at  the 
place  ;  and  to  point  out  the  situations  of  the  several  stars. 

Elevate  the  pole  for  the  latitude  of  the  place  ;  find 
the  sun's  place  in  the  ecliptic,  and  bring  it  to  the  me- 


1 36  Problems, 

ridian,  and  set  the  index  to  12  ;  if  the  time  be  afternoon, 
turn  the  glooe  westward  ;  if  in  the  forenoon,  turn  it 
eastward,  till  the  index  points  to  the  given  hour.  The 
surface  of  the  globe  then  represents  the  appearance  of 
the  heavens  at  that  place. 

1.  Represent  the  appearance  of  the  heavens  for  Jan. 
13,  4  o'clock  A.  M.  and  8  o'clock  P.  M. 

2.  August  30,  at  9  o'clock  P.  M. 

3.  November  3,  at  3  o'clock  A.  M. 

4.  May  16,  at  midnight. 

243.  Prob.  XIX. —  To  find  the  latitude  or  longitude 
of  a  given  star. 

Screw  the  quadrant  on  the  pole  of  the  ecliptic,  bring 
the  star  to  the  meridian,  and  the  degrees  of  the  quadrant 
between  the  ecliptic  and  star,  show  the  latitude,  and  the 
degree  of  the  ecliptic  under  the  graduated  edge  of  the 
quadrant  is  the  longitude. 

1.  What  is  the  latitude  and  longitude  of  Arcturus  .'^ 
Ans. — Latitude  31°  north.     Longitude  201° 

2.  What  "re  the  latitudes  and  longiijfies  of 

Fomalhaut,  Canis  Major, 

Canis  Minor,  Regulus.'^ 


QUESTIONS. 


Sect.  I. 

1  What  does  the  true  Solar  System  consist  of'' 

,2  How  do  primary  planets  and  comets  differ  from  secondary  planeis, 
moons,  or  satellites  ? 

3  How  many  primary  planets  are  there  ? 

4  Name  them. 

5  Hov/  many  secondary  planets  are  there  ? 

6  How  are  they  distributed  ni  the  solar  system  ? 

7  Is  the  number  of  the  comets  known  ? 

8  What  is  the  centre  of  the  solar  system  ? 

9  In  what  direction  do  primary  planets  move  round  the  sun  ? 

10  Wh.  t  is  the  path  of  a  heavenly  body  called  ? 

11  In  w.*iat  direction  do  secondary  planets  revolve  ? 
1'2  Have  comets  a  particular  direction  ? 

13  What  is  the  form  of  the  planets'  orbits  ?  Explain. 

14  Is  the  sun  in  the  centre  ? 

15  What  is  the  lower  focus  ? 16  What  is  the  upper  ? 

17  When  is  a  heavenly  body  said  to  be  in  its  perihelion  ? 

18  When  in  its  aphelion  ? 

19  When  is  the  moon  said  to  be  in  perigee  ? 20  When  in  apogee  ' 

21  What  is  the  eccentricity  of  an  orbit  ?  (see  tig.) 

22  What  is  the  figure  of  all  the  planets,  except  the  Earth  ? 

23  How  is  this  known  of  all  except  the  Earth  ? 

24  How  is  it  known  of  the  Earth  ? 

25  Have  all  the  planets  another  motion  besides  that  round  the  Sun  ." 

26  What  are  axes  ? 

27  Do  large  bodies,  or  small  ones,  generally  turn  quickest  on  their 

axes  f 

28  What  are  the  extremities  of  an  axis  called  ? 

29  Does  the  Sun  ajipcar  to  describe  the  same  circle  among  the  stars, 

which  the  Earth  describes  ? 

30  With  what  difference?  Illustrate. 

31  What  is  this  circle  called  ? 

32  What  is  the  plane  passing  through  this  circle  called.? 

33  How  many  degrees  in  a  circle .'' 

34  How  many  minutes  in  -a  degree  ? 35  Seconds  in  a  mlnuto  ? 

36  How  many  signs  in  the  Ecliptic  ? 

13 


i.38  Questions, 

37  How  many  degrees  in  each  sign  ? 

38  Repeat  the  signs  in  order.    (See  fig.) 

39  In  what  sign  is  the  aphelion  of  each  planet  ?  (See  frontispiece.) 

40  Do  all  the  primary  planets  revolve  in  the  Ecliptic  ? 

41  What  is  the  Zodiac  ?  Describe  it. 

42  Are  all  the  planets  always  in  the  Zodiac .'' 

43  Mention  the  exceptions. 

44  What  are  nodes  ?— — 45  Descending  ? 46  Ascending  ? 

Sect.  IL 

47  By  what  light  are  the  planets  seen  ? 

48  What  does  the   different  distances  of  the  planets  from  the  sun 

occasion  ? 

49  By  what  law  do  heat  and  light  decrease  .'*  Explain. 

50  Can  this  be  proved  ? 51  Prove  it. 

52  What  variation  in  the  appearance  of  the  Sun's  disk  ? 

53  What  does  the   alternate  appearance   and  disappearance  of  spots 

on  the  Sun's  disk  prove  ? 

54  In  what  time  does  the  Sun  turn  on  his  axis? 

55  Do  the  spots  change  in  appearance  .'' 

56  Is  their  cause  known  ? 

57  What  is  the  zodiacal  light  ?  Describe  it. 

58  When  is  it  most  distinct .?        .      '  I  i)/'^ 

59  In  what  region  is  it  always  visible     / 

60  Is  its  cause  known  ? 

Sect.  III. 

61  Proceeding  from  the  sun,  which  is  the  first  planet  ? 

62  What  is  the  mean  distance  of  Mercury  from  the  Sun  .'* 

33  In  what  time  does  it  revolve  round  the  sun  ? — 64  Turn  on  its  axits  ^ 
35  What  is  the  colour  of  its  light  ? 

66  Why  is  it  not  often  seen  ? 

67  Wliat  is  its  greatest  elongatior  .'' 

68  What  is  the  degree  of  heat  and  light  at  Mercury,  compared  with 

that  of  the  Earth  ? 

69  What  would  become  of  water  there  ? 

Sect.  IV. 

70  What  is  the  mean  distance  of  Venus  ? 

71  In  what  time  doos  it  revolve  round  the  sun  f 

72  In  what  time  does  it  turft  on  its  axis  .'* 

73  What  is  said  of  the  light  reflected  by  this  planet  ? 

74  What  is  its  greatest  elongation  ? 

75  What  is  the  comparative  portion  of  heat  and  light  at  Venus  •' 


Questions.  1 39 

76  When  is  this  planet  brightest  ? 

77  What  portion  of  her  disk  is  then  illuminated  ? 

78  What  is  said  of  her  lustre  compared  with  that  of  the  moon .' 

79  From  what  circumstance  docs  this  arise  ? 

80  What  are  called  interior  planets  ? 

81  What  are  called  exterior  planets  ? 

82  When  is  Venus  morning  star  ? — —83  When  evening  ? 

84  Illustrate  this. 

85  If  the  earth  were  stationary,  how  long  would  Venus  be  evening 

star  ? 

86  Illustrate  the  effect  of  the  earth's  motion. 

87  How  long  is  Venus  morning  and  evening  star  .'' 

Sect.  V. 

88  What  is  the  mean  distance  of  the  earth  ^ 

89  In  what  time  does  it  revolve  round  the  sun 

90  In  what  time  does  it  turn  on  its  axis  ? 

91  In  what  time  does  the  moon  revolve  round  the  Earth  .^ 

92  What  is  its  distance  from  the  Earth .'' 

93  In  what  time  does  it  turn  on  its  axis  ? 

94  What  is  the  most  obvious  fact  relating  to  the  Moon .'' 

95  When  is  the  new  moon  exhibited  .'* 9G  When  the  full  moon  ? 

97  When  is  it  said  to  change  .'' 

98  When  is  it  said  to  full  ? 

99  Explain  the  ditferent  i*rtases  of  the  Moon  by  tlie  figure. 

100  When  is  the  moon  sam  to  be  liorned  ^ 

101  When  is  she  said  to  be  in  quadrature  ? 

102  When  gibbous .? 

103  What  phases  does  the  Earth  exhibit,  as  seen  from  the  Moon  ^ 

104  With  what  difference  .? 

105  How  much  larger  does  the  Earth  appear  to  the  Moon  than  tha 

Moon  to  us  ? 

106  What  results  from  the  Moon's  turning  on  its  axis  in  the  same 

time  that  it  revolves  round  the  Earth .'' 

107  What  is  the  consequence  .'' 

108  Describe  the  Moon's  surface,  as  it  appears  through  a  telescope 

109  Of  what  depth  and  width  are  some  of  these  excavations  ? 

110  What  do  these  depressions  probably  resemble  ^ 

111  Are  any  mountains  probably  volcanic  .'' 

Sect.  VI. 

112  At  what  distance  from  the  Sun  is  Mars ' 

1 13  In  what  time  does  Mars  revolve  round  the  Sun  ? 

114  In  what  time  turn  on  its  axis  ^ 

115  What  is  the  colour  of  its  light  .? 


140  (lii-inons, 

J 16  What  is  said  of  the  spots  sometimes  efjcn  on  his  disk  ? 
117  What  is  the  proportion  of  heat  and  light  at  Mars,  compared  with 
ours  ?     ^ 


Sect.  VII. 

118  By  whom  and  whmre  was  Vesta  discovered? 

119  What  is  its  distsuice  from  the  Sun.?    '~, 

120  In  what  time  does  it  revolve  round  the  Sun  ? 

121  Is  the  time  of  turning  on  its  axis  known  ? 

Ask  the  same  questions  respecting  JunOj  Pallas^  and  Ceres. 


Sect.  VIII. 

122  W^hat  is  the  distance  of  Jupiter  from  the  Sun?  (- 

123  In  what  time  does  it  complete  its  revolution  ? 

124  In  what  time  does  it  turn  on  its  axis  ? 

125  What  rank  does  it  hold  among  the  planets  ?  f.y  , 
12'o  What  is  said  of  its  light  ^  .(:.   .  ,  /  :"■ 

127  What  is  the  degree  of  heat  and  light  at  Jupiter  ? 

12S  What  is  its  appearance  when  seen  through  a  telescope? 

129  Do  these  vary  ? 130  Are  they  always  dark? 

131  What  is  said  of  the  spots? 

132  How  many  satellites  has  Jrpiter  ? 

133  Of  what  use  are  their  eclipses? 

134  Hovv^  is  it  ascertained,  that  light  is  8'  coming  from  the  Sun  to 

the  Earth  r 

135  How  are  the  satellites  reckoned  ? 

130  What  is  the  size  of  the  third  ^  Fourth? 

187  Why  could  not  an  observer  in  Jupiter  see  Mars  and  the  interior 

planets  ? 
138  What  advantage  has  a  position  on  Jupiter  over  one  on  the  Earth '^ 


Sect.  IX. 

139  At  what  distance  from  the  Sun  is  Saturn  ' 

140  la  what  time  does  it  turn  on  its  axis  ?      ^ 

141  In  what  time  revolve  round  the  Sun  ?     "; 

142  What  is  the  degree  of  heat  and  light  at  Saturn  : 

143  By  what  is  Saturn  remarkably  distinguished  ? 

144  Describe  the  rings. 

145  How  is  the  surface  of  Saturn  diversified  ? 

146  How  many  satellites  has  Saturn  .^ 

147  How  are  satellites  reckoned: 


Questions.  14  J 


Sect.  X. 

148  When,  and  by  whom  was  Uranus  discovered  r 

149  What  is  its  distance  from  the  Sun  ?    ^ 

150  In  what  time  does  it  revolve  round  the  Sun  P 

151  What  is  the  degree  of  heat  and  light  at  Uraj    n  i 

152  How  many  satellites  has  this  planet  ? 

153  What  is  remarkable  in  the  position  of  their  (   bits  ^ 

154  What  is  their  apparent  motion  ? 

155  To  what  is  this  probably  owing  ? 

156  How  are  they  reckoned  ? 

157  How  is  it  known  that  the  Moon  turns  on  its  axis  in  the  same 

time  that  she  revolves  round  the  Earth  ?  Explain. 

158  What  has  been  observed  of  the  seventh  satellite  of  Saturn  ? 

159  What  does  this  prove  ? 

160  What  is  inferred  from  the  changes  of  Jupiter's  satellites? 

161  What  hence  appears  to  be  a  general  law  of  satellites  ? 

162  What  singular  appearances  hence  present  themselves  to  the  in- 

habitants of  secondary  planets  ? 

163  Illustrate  this. 


Sect.  XI. 

164  What  is  the  general  form  of  comets'  orbits.? 

165  How  did  the  ancients  look  upon  them .'' 

166  What  do  the  moderns  consider  them  ? 

167  How  are  they  generally  distinguished  from  the  other  heavenly 

bodies .? 

168  In  what  direction  do  the  tails  extend .? 

169  Do  comets  vary  in  magnitude  ?  ^ 

170  What  is  said  of  one  which  was  visible  at  Rome  .'' 

171  What  of  the  one  observed  by  Hevelius  .'' 

172  What  is  said  of  their  atmosphere  ? 

173  How  many  have  appeared  since  the  Christian  era  ? 

174  Why  are  the  calculations  of  the  periodical  times  of  comets  ua, 

certain .'' 

175  Who  have  successfully  predicted  the  return  of  comets  .'* 


Sect.  XII. 

176  Is  the  number  of  stars  known  .'* 

177  What  is  the  greatest  number  visible  at  a  time  ? 

178  Why  are  we  deceived  in  the  number  of  stars  visible  at  a  time  r 

179  How  are  they  classed  .? 

180  Why  may  not  the  distance  of  the  stars  be  known .'' 

13* 


142  (Questions, 

181  What  is  supposed  to  occasion,  (partly,  if  not  wholly,)  the  differ- 

ence in  the  appartnt  magnitude  of  the  stars  ? 

182  How  much  more  distant  from  the  Sun  must  the  nearest  star  be 

tKan  the  Earth  is? 

183  Might  the  stars  have  motion  without  its  being  noticed  ? 

184  As  telescopes  are  improved,  what  new  phenomena  are  discovered 

respecting  the  stars  ? 

185  State  the  facts  relating  to  the  stars,  in  No.  50. 

186  What  is  the  Galaxy,  or  Milky-way  ? 

187  What  is  supposed  to  occasion  it  ? 

188  Plow  many  stars  did  Herschel  see  in  i  of  an  hour  ? 

189  What  are  nebula  supposed  to  be  ? 

190  What  are  the  stars  probably  ? 

191  How  is  it  certain  that  they  do  not  reflect  the  Sun's  light,  like 

the  planets  ? 

192  How  are  they  distinguishable  from  the  planets  ? 

193  What  are  Constellations  ? 

194  What  is  said  of  Orion,  and  the  Pleiades  P 

195  W^hat  is  their  number  ? ancient  ? modern  -* 

196  How  are  stars  designated  on  the  globe  ? 

197  How  many  constellations  in  the  zodiac  ? 

198  How  do  these  differ  from  the  si^ns  ? 


CHAP.  II. 

199  What  is  the  Earth's  axis  ? 

200  What  are  the  poles  ? 

201  What  are  celestial  poles  ? 

202  What  is  the  pole  star  ? 

203  What  is  the  equator  ? 

204  What  are  hemispheres  f 

205  What  is  the  celestial  equator  ? 

206  From  what  is  latitude  reckoned ." 

207  What  are  parallels  of  latitude  ? 

208  Is  the  number  of  parallels  limited  ? 

209  What  is  a  meridian  ? 

210  Is  the  number  of  meridians  limited  ? 

21 1  When  are  places  said  to  be  in  different  longitudes : 

212  What  are  celestial  meridians  ? 

213  When  it  is  noon  at  any  place,  where  is  the  sun  ? 

214  Illustrate  what  has  been  said  by  the  figure. 

215  How  is  the  latitude  of  a  place  on  the  earth  estimated  ? 

216  Illustrate  this  by  the  figure. 

217  How  is  the  longitude  of  one  place  from  another  estimated^ 
1.13  Illustrate  this. 

210  What  is  a  Great  Circle  ? 

220  What  are  Less  Circles  .? 


Qu 


143 


221  Is  the  equator  a  great  or  a  less  circle  ? Why  ? 

222  Are  parallels  great  or  less  circles  ? Why  ? 

223  Are  meridians  great  or  less  circles  ? Why  ? 

224  Is  there  any  natural  reason,  why  longitude  should  be  r^koned 

from  one  meridian,  rather  than  from  another  ? 

225  What,  till  lately,  has  been  the  custom  of  writers  ? 

226  From  what  prime  meridian  is  longitude  now  usually  reckoned  ? 

227  What  is  the  greatest  latitude  a  place  can  have  ?  Why  ? 

228  What  is  the  greatest  longitude  a  place  can  have  ? 

229  From  what  is  latitude  of  heavenly  bodies  reckoned  ? 

230  What  are  secondaries  to  the  ecliptic  ? 

231  What  are  the  Poles  of  the  Ecliptic  ? 

232  How  far  are  they  distant  from  the  celestial  poles  ? 

233  How  is  the  longitude  of  a  heavenly  body  reckoned  ? 

234  From  what  point  of  the  ecliptic  ? 

235  What  is  the  declination  of  a  heavenly  body  ? 

236  What  is  right  ascension  ? 

237  State  the  difference  between  celestial  latitude  and  declination. 

238  State  the  difference  between  longitude  and  right  ascension- 

239  Are  degrees  of  latitude  of  the  same  absolute  length  ? 

240  What  is  that  length  ? 

241  Are  degrees  of  longitude  of  the  same  absolute  length? 

242  Explain  the  reason. 

243  What  is  the  rule  ? St,e  Italics. 

244  What  is  the  horizon  ? 

245  What  is  the  difference  between  the  sensible   horizon  and  the 

rational  ?     Explain. 

246  Why  is  not  the  difference  perceptible  ? 

247  In  this  treatise,  which  is  meant  when  the  term  occurs  ? 

248  What  is  the  Zenith  ? 

249  How  far  is  it  from  the  horizon  ? 

250  What  is  the  Nadir  ? 

251  What  are  the  zenith  and  nadir  sometimes  called  ? 

252  How  far  is  the  zenith  from  the  celestial  equator  •* 

253  Illustrate  this  by  the  figure. 

254  If  the  distance  of  the  zenith  from  the  celestial  equator  be  found, 

what  does  it  show  ? 

255  Does  the  plane  of  the  horizon  change  its  position  as  a  person 

changes  his  place  ? 

256  Illustrate  this  by  the  figure. 

257  Hence  to  find  the  distance  of  the  zenith  from  the  celestial  equa- 

tor, what  is  necessary  ? 

258  Illustrate  the  use  of  the  quadrant. 

259  How  can  latitude  be  found  by  day  .'' 

260  Illustrate  this. 

261  If  the  sun  be  not  in  the  celestial  equator  what  is  necessary  ^ 

262  Illustrate  this  by  examples. 

263  VvHiat  is  the  rule  respecting  declination  ? 

%{]\  What  is  the  common  way  of  ascertaining  longitude  ? ,■ 


144  (^lestions, 

265  Why  is  not  this  to  be  depended  upon  ? 

266  How  many  degrees  does  the  sun  appear  to  pass  through  in  an 

hour  ? 

267  Do  clocks  differ,  as  places  are  in  different  longitude  ? 

268  Illustrate  this. 

269  How  can  longitude  be  known,  by  having  the  difference  of  time  ? 

270  Illustrate  this. Tico  excnnples.     .Vo.  76. 

271  What  is  the  difficulty  in  this  method  ? 

272  What  machines  are  most  uniform  in  their  moTements' 

273  Why  may  not  these  be  used  at  sea  ? 

274  Why  may  not  watches,  &c.  be  made  accurate  meai^^^ers  of  tanc  ? 

275  How  can  time-pieces  be  corrected  at  sea  ? 

276  Illustrate  by  an  eclipse  of  the  moon. 

277  How  frequently  is  there  an  eclipse  of  a  satellite  of  Jupiter  ? 

278  Why  may  not  time-pieces  be  corrected  by  these  eclipses  ? 

279  What  other  method  of  correctingr  time-pieces  is  mentioned  ? 
2S0  Explain  the  use  of  the  tables. 

281  What  is  still  a  great  desideratum  ? 

282  What  encouragement  have  the  English  given,  to  direct  the  at- 

tention of  astronomers  to  this  subject  ? 

283  Have  any  rewards  been  yet  obtained .' 

284  What  is  now  the  greatest  reward  which  can  be  obtained  ^ 


CHAP.  III. 


Sect.  I. 

285  What  is  the  direct  motion  of  a  planet .' 

286  What  is  retrograde  motion  : 

287  When  is  the  motion  of  Venus  direct  ?     (See  fig.) 

288  When  is  it  retrograde  .- 

289  When  is  Venus  stationary  ? 

I^jO  When  is  Venus  in  her  superior  conjunction  .' 

291  Vv'hen  in  her  inferior  conjunction  r 

292  When  is  the  motion  of  the  Earth  seen  from  Venus  direct .' 

293  When  retrograde  .'  Illustrate. 

294  When  is  the  Earth  m  opposition  ? 

295  When  in  conjunction.' 

296  What  motion  does  each  exterior  planet  exhibit  to  us  ? 

297  Does  Venus  and  the  other  planets  vary  their  apparent  magnitude  ? 

298  What  is  the  cause  of  this  variation  .' 

299  When  does  an  eclipse  of  the  Sun  take  place  .' 

300  When  does  an  eclipse  of  the  Moon  take  place  ? 

301  At  the  time  of  an  eclipse,  where  must  the  Sun,  Earth,  and  Moon 

be- 


Questions.  145 

302  Why  does  not  an  eclipse  take  place  at  every  full  and  new  Moon  ? 

303  At  new  or  full  Moon,  how  near  must  the  Moon  be  to  the  ecliptic 

to  occasion  an  eclipse  ? 

304  To  eclipse  the  Sun,  how  near  a  node  must  the  Moon  be,  at  the 

time  of  change  ? 

305  To  eclipse  the  Moon,  how  near  a  node  must  she  be  at  the  time 

of  full  ? 

306  Is  the  Sun  or  Moon  oftenest  eclipsed  ? 

307  Why  do  the  inhabitants  of  any  particular  place,  as  Bo&ton,  wit- 

ness more  lunar  than  solar  eclipses  ? 

308  What  is  the  figure  of  the  earth's  shadow  ? 309    Why  ? 

310  Does  the  Moon's  shadow  ever  fall  upon  a  hemisphere  of  the 

earth  ? 

311  Does  the  Moon's  shadow  ever  terminate  before  it  reaches  the 

Earth  ? 

312  When  is  an  eclipse  said  to  be  annular? 

313  When  total? 

314  When  partial? 

315  What  is  the  penumbra  9 

316  What   would  be   the  appearance  to  a  person,  if  he  could  pass, 

during  an  eclipse,  from  o  to  D  9 

317  Is  the  inner  or  outer  region  of  the  penumbra  darkest  ? 

318  Under  the  most  favourable  circumstances,   on  what  portion  of 

tiie  Earth's  hemisphere  does  the  penurnbra  fall  ? 

319  What  is  the  consequence  ? 

320  IIuw  is  the  case  uitierent  in  lunar  eclipses  ? 

321  What  is  the  consequence  ? 

322  Explain  the  reason,  why  a  lunar  eclipse  is  visible  to  all  to  whom 

the  moon  at  the  time  is  visible  ;  and  why  a  solar  one  is  not. 

323  Is  it  diihcult  to  tell  the  precise  time  when  a  lunar  eclipse  begins 

or  ends  ' 324    Why  ?  . 

325  Is  the  case  similar  in  solar  eclipses  ? 

326  Does  one  primary  planet  ever  enter  into  the  dark  shadow  of 

another  ? Why  ? 

327  Is  the  passage  of  a  superior  planet  through  the  Earth's  penurnbra 

perceptible  to  us  ? Why  ? 

328  If  the  Moon's  nodes  were  stationary,  how  often  would  one  come 

between  the  Earth  and  Sun  ? 

329  How  often  must  an  eclipse  of  the  Sun  take  place  ? 

330  Explain  the  reason. 

331  Is  the  same  true  with  regard  to  lunar  eclipses  ? Why  r 

332  Are  the  Moon's  nodes  stationary  ^ 

333  How  often  may  a  node  be  between   the   Sun   and  Earth  in  one 

year  ? 

334  Hnw  lonof  are  they  in  completing  a  revolution.'' 
';35    Wiiat  is  the  common  number  of  eclipsej  in  a  year ' 
.j3()    Vvhat  is  the  smallest  number? 

?'X7   Wliat  is  the  greatest.'^ 
S3i3    What  are  dlo-its? 


146  Questions. 


Sect.  II. 

339  What  does  common  experience  show  ? 

340  In  what  case  is  this  effect  striliing  ? 

341  What  occasions  day  and  night .'' 

342  If  the  line  JVS  were  always  in  the  circle  dividing  the  light  from 

the  dark  hemisphere,  what  would  be  the  consequence  ? 

343  Illustrate  this. 

344  When  is  A''S  in  this  position  ? 

345  What  periods  are  called  equinoxes  ? 

346  Which  vernal  ? autumnal  ? 

347  At  the  equinoxes,  where  and  when  does  the  Sun  rise  ?  set  ? 

348  At  other  seasons,  what  is  the  position  of  JVS  f 

349  Illustrate  the  effect  of  this  position  when  the  Earth  is  at  Can- 

cer.  W^hen  at  Capricorn. 

350  In  all  positions^vhat  is  fact  at  the  equator  '' 

351  When  days  are  longest  in  N.  latitude, -how  are  they  in  south. 

Vice  versa  ?    . 

35*2  How  many  days  and  nights  in  a  year  at  the  poles  ? 

353  How  far  beyond  a  pole  can  the  Sun  shine  .'' 

354  What  are  Polar  Circles .? 

355  What  are  the  Tropics  ? Of  Cancer  ? Of  Capricorn  ^ 

356  What  are  the  Solstices  P 

357  At  the  summer  solstice,  how  are  days  and  nights  in  N.  latitude  ? 

In  S.  latitude  ' 

358  At  the  winter  solstice,  what  is  the  case  ? 

359  Explain  the  reason  why  the  Earth  tmrns  on  its  axis  once  more 

in  a  year  than  we  have  days. 

360  What  IS  a  Sideiial  day  .? 

361  What  IS  a  Solar  or  Natural  day  ? 

362  W^hat  is  the  difference  between  the  'periodical  and  synodical 

revolution  of  the  Moon  ?  (See  small  print.) 


Sect.  III. 


Art.  1. 

363  At  what  rate  does  light  move  ? 

364  At  what  rate  does  the  earth  move  in  its  orbit  ? 

365  What  results  from  these  two  motions  ?  Illustrate. 

366  What  does  aberration  amount  to  ? 


Quesiicns.  147 


Art.  2. 

367  Does  the  Earth  receive  a  greater  degree  of  heat  and  light  from 

the  Sun  at  one  time  than  at  another  ? 

368  Illustrate  this. 

369  Does  this  occasion  the  seasons?     .  / 

370  What  does  occasion  the  seasons  ?  Illustrate. 

371  What  is  the  cause  of  the  different  obhquity  of  tliG  Sun's  rays  ? 

372  Explain  this  effect  from  Nos.  110  ai  J  11 1. 

373  What   other   circumstance   contributes  much  to  tiie  warmth  of 

summer,  &c.  ? 

374  In  summer  is  the  sun  more  powerful  in  S.  latitude  than  m  N.  ? 

Why  ? 

375  What  compensation  for  this,  in  north  latitude  ?  Explain. 

376  How  much  longer  are  summers  in  north  latitude  than  in  south  .^ 

377  Why  do  we  not  have  the  greatest  heat  and  Qold  at  the  solstices^ 

378  When  is  our  warmest  weather  ? coldest  ? 

379  What  part  of  the  day  is  warmest  ? 

380  W^hat  is  the  difference  between  a  siderial  and  a  solar  year  ? 


Art.  3. 

381  When  is  the  Sun  said  to  be  slow  of  the  clock  ? 

382  When  fast  of  the  clock  ? 

383  What  is  mean  time  ? Apparent  time  ? Equation  ? 

384  What  is  the  first  cause  of  the  inequality  of  natural  days .' 

385  What  was  ascertained  by  Kepler  ^ 

386  How   does  it  thence  follow,  that  the  Sun  must  pass  through  a 

greater  portion  of  his  orbit  in  some  days  than  in  others  .? 

387  Illustrate  this.     (No.  118.) 

388  Because  the   Earth  advances  in  its  orbit   farther  in  some  days 

than  in  others,  how  does  it  thence  follow  that  some  days  must 
be  longer  than  others .''  (No.  119.) 

389  So  far  as  this  cause  operates,  when  would  the  Sun  and  clock 

agree  ^ 

390  What  is  the  second  cause  of  the  inequality  of  natural  days  ? 

391  Illustrate  this.     (Nos.  121  and  122.) 

392  So  far  as  this  cause  operates,  when  would  the  Sun  and  clock 

agree  ^ 

393  During  what  part  of  the  year  would  the  Sun  be  fast  of  the  clock  <* 

394  When^slow  of  the  olock  .? 

395  How  often,  and  when,  do  the  Sun  and  clocks  actually  agree  .'* 

396  What  is  the  greatest  possible  ditference  between  mean  and  ap- 

parent time  .'* 

397  When  does  this  take  place  .»* 


48  Questions. 


Art.  4. 

398   What  is  Ih 3  mean  daily  difference  in  the  times  of  the  Moons 

rising  ? 
309    What  was  early  observed  by  the  husbandman  ? 

400  Explain  the  cause  of  the  harvest  Moon.     (No.  126.) 

401  Why  do  wc  not  notice  these  variations  in  the  Moon's  rising  at 

other  seasons .'' 

402  What  wonderful  accommodaticn  to  the  wants  of  the  inhabitants 

in  the  polar  regions  ir  noticed  ? 

403  Do  ^he  inhabitants  in  south  latitude  have  harvest  Moons  ? 

404  How  do  they  differ  from  ours  } 

405  Does  the  inclination  of  the  Moon's  orbit  to  the  ecliptic  vary  the 

effects  just  treated  of? 

406  When  are  these  effects  increased  ?  When  diminished  ? 


Sect.  IV. 

407  When  is  a  ray  of  light  said  to  be  refracted  ? 

408  Illustrate  this. 

409  What  two  circumstances  augment  refraction  ^ 

410  What  familiar  experiment  illustrates  refraction  ? 

411  If  a  ray  of  light  pass  through  a  medium,  the  density  of  which 

increases  downwards,  what  line  will  it  describe  ? 

412  Since  the  atmosphere  is  such  a  medium, what  is  the  consequence  ? 

413  In  what  direction  do  we  see  objects .'' 

414  What  is  an  obvious  effect  of  refraction  ? 

415  Can  the  inhabitants  of  Boston  ever  see  the  sun  and  planets  in 

their  true  place  ?  Why  ? 

416  Does  refraction   make  heavenly  bodies  appear  higher  or  lower 

than  they  really  are  ? 

417  Illustrate  this. 

4  '8    W^hat  singular  phenomenon  does  this  account  for  ? 

419  How  does  this  affect  the  length  of  the  day  .'* 

420  Making  how  much  in  a  j^ear  ^ 

421  Is  this  effect  the  same  at  all  places  ^ 

422  What  is  twilight  ? and  what  occasions  it? 

423  When  does  it  commence  and  end  ^ 

424  What  occasions  variation  in  the  duration  of  the  twilight  ? 

425  As  latitude  increases,  how  is  the  duration  of  twilight  affected  ? 

426  Is  it  longer  at  one  season  than  at  another  ^ 

427  When  is  twilight  longest,  and  when  shortest  at  Boston  .'* 

428  What  is  the  first  appearance  of  morning  twilight  usually  called.^ 

429  Is  the  evening  or  morning  twilight  longest  ^  Why  .? 

430  Were  there  no  atmosphere,  what  appearances  would  take  pla^Ce  ? 

431  When  is  refraction  greatest  ^ 


(^estions,  149 

432  How  does  this  fact  account  for  the  Sun  or  Moon  appearing  oval 

in  the  horizon  ? 

433  When  the  Moon  is  eclipsed,  what  renders  it  visible  ? 

434  Are  objects  on  earth,  as  well  as  heavenly  bodies,  elevated  by  re 

fraction  ?  Why  ? 

435  What  is  the  most  striking  effect  of  this  kind  ? 

436  From  what  is  the  horizontal  moon  supposed  to  result  ? 

437  What  appears  to  be  the  figure  of  the  sky  ? 

438  In  judging  of  the  unknown  size  of  an  object,  what  do  we  first 

determine  ? 

439  Illustrate  this. 

440  Do  intervening  objects  assist  us  in  judging  of  distance  ? 

441  Explain   how  this  fact  makes  the  Moon  appear  more  distant  in 

the  horizon  than  in  the  zenith. 


Sect.  V. 

442  What  is  Parallax  ? 

443  Illustrate  parallax  by  the  figure  ;  also,  true  place,  and  apparent 

place. 

444  Is  parallax  greatest  when  the  body  is  in  the  horizon,  or  in  the 

zenith  ? 

445  How  does  distance  affect  parallax  ? 

446  Does  parallax  elevate  or  depress  bodies  ? 

447  What  is  annual  parallax  ? 

448  Have  the  fixed  stars  any  apparent  parallax  : 

449  How  much   more  distant  from  our  Sun  must  they  be,  than  we 

arc  .'*     - 

450  Illustrate  how  the  distance  of  the  Moon  from  the  Earth  ma)  be 

obtained. 

451  Did  the  ancients  know  the  distance  of  the  Earth  from  the  Sun  ? 

452  How  was  the  first  approximation  to  the  truth  obtained  ? 

453  Illustrate. 

454  Why  was  not  this  method  to  be  relied  on  ? 

455  What  method  did  Dr.  Halley  devise  ? 

456  What  is  the  first  mentioned  subject  which  Astronomers  had  de 

termined  by  observation  ? 

457  What  law  is  stated,  developed  by  Kepler  ? 

458  From  this  what  could  be  readily  found  ?   Example. 

459  What  is  the  third  mentioned  subject .'' 

460  What  i\\Q  fourth? 

461  Illustrate  (Nos.  153  &  154)  how  the  parallax  of  the  Sun  can  be 

obtained. 

14 


'  ^^  Questions^ 


BOOK  II. 

4G2  What  property  is  common  to  every  particle  of  matter  r 

463  What  is  this  tendency  called  ? 

464  Does  it  differ  from  weight  ? 

465  When  we  say  a  body  weighs  a  pound,  what  do  we  mean  ^ 
406  Is  this  tendency  uniform  ? 

467    What  is  the  law  by  which  it  varies  ? 
^i:)S    Illustrate  tliis. 

469  How  do  bodies,  containing  a  different  number  of  particles,  affect 

each  other  ?  Illustrate. 

470  Is  all  attraction  mutual  ? 

471  What  is  the  centre  of  gravity  of  two  bodies  ? 

472  How  can  this  be  found  ? 

473  What  other  universal  circumstance  attends  inanimate  bodies? 

474  111 usf rate  inertness. 

475  State  the  two  universal  facts  relating  to  matter. 


Sect.  I. 

476  Supposing  a  planet  in  motion,  how   could  gravity  cause  it  to 

revolve  in  a  circle  .'' 

477  How  in  an  ellipse  ? 

478  Explain  why  the  former  orbit  is  a  circle. 

479  When  do  the  centripetal  and  centrifugal  forces  balance   each 

other  ? 

480  Explain  why  the  latter  orbit  is  an  ellipse. 

481  Does  the  Sun  revolve  around  the  centre  of  gravity,  as  well  as 

the  Earth  I 

482  Is  the  Sun's  motion  regular  ?  Why  .'* 

483  Doss  the  Moon  also  revolve  round  a  centre  of  gravity .'' 

484  How  far  distant  from  the  Eartli's  surface  is  the  centre  of  gravity 

of  the  Earth  and  Moon  ? 

485  What  has  been  ascertained  with  regard  to  double  stars  .'' 

486  What  has  Dr.  Herschel  fourid  ? 

487  Have  the  stars  a  peculiar  motion  ? 
488,,  How  did  Dr.  Halley  first  discover  this  .'' 
4S^    AVhat  is  this  motion  of  the  stars  called .'' 

490  What  facts  seem  to  prove  that  the  Sun  has  a.  proper  motion  .'' 

491  Towards  what  part  of  the  heavens  does  this  ijiotion  appear  to  be 

directed  .'' 

492  What  beautiful  supposition  of  Herschel  is  mentioned  ? 

493  What  is  probable  with  regard  to  nebulae  .'' 

494  To  complete  the  analogy  of  the  universe  what  is  necessary  .-' 


*      ■"  Questions.  151 

-.-:..    ^' 

Sect.  II. 

495  Explain  the  cause  of  the  retrograde  motion  of  the  Moon*s  nodes 

Sect,   III. 

496  What  is  an  obvious  effect  of  mutual  attraction  and  change  of 

distance  ? 

497  Illustrate. 

498  Before  the  new  planets  were  discovered,  did  astronomers  sus- 

pect their  existence  ?     Why  ? 

499  Nearly  how  many  corrections  are  necessary  to  find  the  Moon's 

true  place  ? 

500  Explain  the  effect  of  the  varying  attraction  of  the  Sun  on  the 

Moon  and  Earth  ?  * 

501  Point  out  the  octants  of  the  Moon's  orbit :  syzygies. 

502  In  what  points  of  her  orbit  is  the  Moon  too  fast  ? too  slow  ? 

503  In  what  point  does  she  move  at  her  mean  rate  ? 504  More 

than  her  mean  rate  ? 505  Less  than  her  mean  rate  ? 

506  Why  is  a  lunation  longer  in  winter  than  in  summer  ? 

507  How  much  longer  is  it  ? 

508  What  fact  is  stated  as  recorded  in  history  '' 

509  When  did  the  eclipse  commence  according  to  our  tables  ^ 

510  Why  might  not  the  ancients  be  mistaken  in  the  time  ? 

511  From  this  and  other  discordances  what  is  the  conclusion? 

512  What  did  this  fact  lead  astronomers  to  suppose  r 

513  What  did  La  Place  discover  to  he  the  cause  ? 

514  What  else  did  La  Place  discover  ^ 

515  What  class  of  bodies  are  most  disturbed  ?     Why  ? 

516  How  much  was  the  comet  of  1682  retarded  by  Jupiter  and  Sa- 

turn ? 

517  Are  planets  in  like  manner  disturbed  by  comets  .'*. 

518  State  the  circumstances  which  prove  this. 

Sect.  IV. 

519  What  is  the  cause  of  the  spheroidal  figure  of  the  Earth  and 

planets  ? 

520  Illustrate  this. 

521  How  much  greater  is  the  diameter  of  the  Earth  through  the 

equator,  than  through  the  poles  ? 

522  What  striking  fact  results  from  this  figure  of  the  Earth  ? 


152  '  Questions. 


Sect.  V. 

523  What  is  the  precession  of  the  equinoxea  ? 

524  Explain  the  cause  of  it. 


Sect.  VI. 

525  What  are  Tides  ? 

526  What  occasions  them  ? 

527  Illur-,rate. 

528  In  what  region  of  the  Earth  are  tides  highest? 

529  What  effect  does  the  Sun  actually  have  on  the  tides; 
"530  What  are  Sprang  Tides  ? 

531  What  are  Neap  Tides  ? 

532  In  what  time  of  the  year  are  tides  highest?      Why? 

533  What  occasi-^ns  inequality  in  the  tides  at  places  equally  subject 

to  the  Mooii  ti  action  ? 

534  At  what  places  are  tides  very  high  ? 

535  How  much  higher  are  waters  in  the  Red  Sea  than  in  the  Medi- 

terranean ?        C' 

536  Why  are  the  tides  small  in  the  Mediterranean  and  Baltic? 

537  What  is  remarkable  in  the  river  Severn  ? 

538  What  in  the  river  Thames  ? 

539  What  in  the  river  Amazon  ? 


THS   END 


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